Search results “Matrix element product”

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GeeksforGeeks

Multiplying two 2x2 matrices.
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/multiplying_a_matrix_by_a_matrix?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

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Khan Academy

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Vidya Sagar

The direct product is a way to combine two groups into a new, larger group. Just as you can factor integers into prime numbers, you can break apart some groups into a direct product of simpler groups.
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Socratica

Showing that matrix products are associative
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/composition_of_transformations/v/distributive-property-of-matrix-products?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Khan Academy

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: http://ocw.mit.edu/RES-18-009F15
Instructor: Gilbert Strang
A positive definite matrix has positive eigenvalues, positive pivots, positive determinants, and positive energy.
License: Creative Commons BY-NC-SA
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More courses at http://ocw.mit.edu

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MIT OpenCourseWare

Check us out at http://math.tutorvista.com/algebra/matrix-multiplication.html
Matrix Multiplication
The ordinary matrix product is the most often used and the most important way to multiply matrices. It is defined between two matrices only if the width of the first matrix equals the height of the second matrix. Multiplying an m×n matrix with an n×p matrix results in an m×p matrix. If many matrices are multiplied together, and their dimensions are written in a list in order, e.g. m×n, n×p, p×q, q×r, the size of the result is given by the first and the last numbers (m×r), and the values surrounding each comma must match for the result to be defined. The ordinary matrix product is not commutative.
The element x3,4 of the above matrix product is computed as follows
The first coordinate in matrix notation denotes the row and the second the column; this order is used both in indexing and in giving the dimensions. The element at the intersection of row i and column j of the product matrix is the dot product (or scalar product) of row i of the first matrix and column j of the second matrix. This explains why the width and the height of the matrices being multiplied must match: otherwise the dot product is not defined.
The figure to the right illustrates the product of two matrices A and B, showing how each intersection in the product matrix corresponds to a row of A and a column of B. The size of the output matrix is always the largest possible, i.e. for each row of A and for each column of B there are always corresponding intersections in the product matrix. The product matrix AB consists of all combinations of dot products of rows of A and columns of B.
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TutorVista

Do matrix arithmetic in R.
Join DataCamp today, and start our interactive intro to R programming tutorial for free: https://www.datacamp.com/courses/free-introduction-to-r
Throughout the exercises on matrices, you have already bumped into the `colSums()` and `rowSums()` functions. The `colSums()` function, for example, took the sum of each column, and stored the result in a vector. Apart from these matrix-specifc math functions, you can also do standard arithmetic with functions. Remember how you could do all the typical arithmetic operations on vectors? Again, it's exactly the same thing for matrices: all computations are done element-wise.
Ever heard about that other classic trilogy, the Lord of the Rings? As for Star Wars, you can build a matrix of box office revenue for both US and non-US regions. The information is saved in the the matrix, lotr_matrix, which has been constructed as follows:
These are astronomical numbers, we're talking about millions of US dollars here. What if you wanted to convert this to Euros? At the time of writing, 1 euro converts to 1 point 12 US dollars, so to convert the figures to euros, we'll have to divide the figures by 1.12. We can simply use the division operator as if we were performing the division on a single number:
R performs the operation element-wise: each element is divided by 1.12. This works just the same for multiplication, summation and subtraction. Say, for example, that the theaters world-wide claim 50 million dollars on the box office revenue. How much is left for the Lord of the rings concern itself then? We simply subtract 50 from LOTR matrix:
Operating on matrices with single numbers looks pretty straightforward, and this actually also holds when you're performing calculations with two matrices. Suppose that instead of demanding the same sum of money for every release, theaters worldwide ask for 50 million for the first release, 80 for the second and 100 for the third. We could build a matrix, say, `theater_cut`, with the same dimensions as LOTR matrix, that looks as follows
If we now subtract theater_cut from LOTR matrix:
This time, the substraction was also performed element wise: the figures for the Two towers lowered by 80, while the figures for the return of the king were lowered by 100. Makes perfect sense right?
Now, what would happen if we use a vector, containing 50, 80 and 100 to subtract from the lord of the rings matrix? Let's try it out.
The result is exactly the same! That's because once again, R performed recycling. R realizes that the dimensions of the matrix and the vector don't match. Therefore, the vector is extended to a matrix of the same size, and is filled up with the vector elements column by column. The matrix that is thus actually subtracted from the lotr matrix is the following:
This matrix is the exact same one as we built manually before, so the result is the same. Again, blindly trusting R that it performs recycling just the way you want it can be quite a dangerous practice. You should be fully aware of how this recycling is actually happening.
If you are familiar with linear algebra, you might wonder how matrix multiplication would work. Well, in R, multiplication is simply performed element wise. Suppose you want to convert the US dollar figures to euros with the exchange rate at the time of the release, you can again create a new matrix, this time with the amount of euros you should pay for 1 dollar.
Now, we can simply multiply the lord of the rings matrix with the rates matrix:
Again, every calculation is done element-by-element. The top left figure has been multiplied by one point 11, while the bottom right figure was multiplied by point 82.
To end this last video on matrices, I want to stress once more that matrices and vectors are very similar: they simply are data structures that can store elements of the same type. The vector does this in a one-dimensional sequence, while the matrix uses a two-dimensional grid structure. Both of them perform coercion when you want to store elements of different types and both of them perform recycling when necessary. Similarly, vector and matrix arithmetic are straightforward: all calculations are performed element-wise. That's all folks. Time to wrap up on matrices in the following exercises and I'll be awaiting you to explain all about factors!

Views: 26462
DataCamp

Matrix entry or element, matrix size or dimension, double subscript, matrix addition and subtraction, scalars and matrices, multiplication of a scalar and a matrix, dot product or inner product, matrix product as a collection of dot products

Views: 110
Omnia A

C Program to find the sum of all diagonal elements of a given matrix.
Loop variable i - represents rows
Loop variable j - represents columns
diagonal elements are those where indexes i==j

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Sundeep Saradhi Kanthety

How to do element-wise (Hadamard product. Schur product) multiplication and conventional matrix multiplication in R

Views: 4719
Phil Chan

How to do element-wise (Hadamard product. Schur product) multiplication and conventional matrix multiplication in R

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Phil Chan

The operation of matrix multiplication is defined for a pair of matrices (let's call them "left" and "right") with the only requirement - the number of elements in each row of the left matrix (left operand) in an operation of multiplication must be equal to a number of elements in each column of the right matrix (right operand). In other words, if the sizes of these two matrices are KxL for the left operand (that is, it has K rows and L columns) and MxN for the right operand (M rows and N columns) , then L must be equal to M. The reason for this requirement is the necessity to form a scalar product of row-vectors that form rows of the left operand with column-vectors that form columns of the right operand, as we did in the examples above, and scalar product is defined only for two vectors of the same dimension.
Now, if a KxM matrix A=[aij] is multiplied by an MxN matrix B=[bmn], the result, by definition, will be a KxN matrix C=[ckn] with elements calculated as a scalar (dot) product
ckn = ak*·b*n
where ak* is a k-th row-vector of a matrix A and b*n is a n-th column-vector of a matrix B.
Finally, let's recall how we came to a formula for matrix product in 2x2 and 3x3 cases of matrix size. We wanted two consecutive linear transformations represented by two matrices A and B to be replaced by one transformation represented by a matrix C that we called the product of two initial matrices. That is C, by definition, was called the result of a new matrix operation A·B. All we needed was to find such a matrix C for any two given matrices A and B, which we did and the formula for each element of the matrix C was
ckn = bk*·a*n
where bk* is a k-th row-vector of a matrix B and a*n is a n-th column-vector of a matrix A.
As a result of such a definition, we wrote the equivalence of two transformations by A and B with one transformation by their product A·A as
B(Av) = (B·A)v
We know now that a linear transformation of a vector by a matrix constitutes the multiplication of that matrix by a column-vector viewed as Nx1 matrix. In this light the formula above is just an associative law of matrix multiplication. So, to derive with a reasonable formula for multiplication of two matrices we used, as a necessary property of this operation, its associativity - a very reasonable requirement indeed.
In other words, linear transformation of vectors was viewed as a matrix multiplication of the NxN square matrix by a column-vector interpreted as the Nx1 matrix; and a composition of two linear transformations being equivalent to one, their matrix product, is an associative property of the operation of multiplication. These considerations lie in the foundation of the definition of matrix multiplication.

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VID.education

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For more cool math videos visit our site at http://mathgotserved.com or http://youtube.com/mathsgotserved Good day students welcome to mathgotserved.com in this clip were going to be going over how to find and verify inverse a square matrix forget to visit our website at mathgotserved.com for access to a wide variety of tutorials ranging from algebra and calculus so we only get started let's go over what the formula is finding the inverse of the matrix okay so the formula you matrix a square 2 x 2 matrix is a b c d Dan -1 is going to be one over the determinant of a multiplied by what you gets we take the industries the diagonals DA and take the opposite of the week negative see negative okay so this is the formula for finding the then the inverse the inverseof the matrix I don't forget that's the determinant of matrix a is given by 4 x 2 matrix it is a product of the diagonal a D this is the diagonal right here ab minus the product on the way to the wings right here DC okay you want to note in the determinant of a is equal to zero guess what then eight to that into the negative one is not to find so that if the degrees tells us that the matrix is not vertical if it has is zero determine what I that the inverse only matrix to determine it was never be zero okay so let's keep that in mind go ahead and try example 1 so we are to find the inverse and verify that our answer is correct okay so why inverse it is negative one and verify your answer where all matrix a is equal to 2143 okay so there goes your matrix a isolate and find the inverse first remember the full authority inverse it's one over a D minus DC 100 and determinant isolate you get when you switch the diagonals DA 18 the opposite of the wings needed be negative see I so let's see what easy and the artist is a right here a the see the simplify the inverse relationship the following are going to do one over 8080 is 2×3 which is six minus DC which is for multiplied byif we switch a and d will have three to and opposite of one for your one and name for I we were further will have one over to times three -4 -1 2000 is simply distributes to into the entire into the elements of this matrix so can distribute to the one half we have three over to minus forward to minus one over to and then positive to over to the reduced form of this matrix is three over to -2 minus one half into over to is one so this is my inverse a today negative one were also asked to verify that our solution is correct to accomplish this with going to do a check in our check is in in most multiplying a of this inverse and that she give us the identity major so let's see that's what happens here matrix eight this rewrite matrix is to one or three and matrix the only a inverse right is three over two negative one half negative to and one so want to see the product of these two is equal to the identity matrix? Is it equal to the identity matrix 1001 this is the identity matrix for 2 x 2 matrix now let's go ahead and multiply and set up my multiplication bars I like to multiply using a different method so on when a line with my rules of this colony; in this right here so my rules from matrix a to come of four and then the second row one, three negative take my my columns from matrix the inverse and line them up horizontally so we have three over to, negative one half and -2, one okay so what is going to just multiply X is an wise and by the sum so three over to times two is 3+ negative one half times four is positive actually negative negative to be -2 is one of multiply these two make coordinates -2 times positive to the -41×4 is for the sum is it to this to one faster over to the to three that's negative one half -3 over to the sum is zero and then the last set one and negative to is negative to 1×303 the sum is one so we can see that the product off a and the resulting dots resulted in the identity matrix so with confidence that our solution is in fact correct okay so let's talk our answer a inverse equals three over to negative to negative one half and one so that's that the thanks so much for taking the time to watch this presentation really appreciated feel free to subscribe to my channel for updates to other cool tutorials such as this and and comments section you have any questions or any problems you why +2 make tutorials on this post it in the comments section is there any suggestions you have for us to improve our tutorials to assist you in the classroom mathematics these negative comments section also you can also visit our [email protected] as indicated earlier to get axis so what to write simply tutorials ranging from algebra to calculus and people watching and have a wonderful day

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maths gotserved

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Jdm Garage

Hey guys! In this video I am showing you how to make a matrix in Python. If you like this video.
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TECH PHASE

you can download source code from here
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Coding Xpertz

In this Video Dr. Vivek Bindra explains the 3 steps to build your product strategy. Through this video , he guides the business class to learn to select the right customers | audience for their business. He says it is very important to understand the demographics|psychographics of the audience. He further says that during the initial days of the business, a wrong customer can kill the liquidity in your business. Acquisition of the wrong customer is very harmful for thee business due to delayed payments, defaults in payments etc. It is further important to identify the right product mix ( High focus | Low focus | No focus ) products in your business. He has also given his audience an unique RISIMIS formula ( Ritual of Sixty Minute Solitude ). Next he explains in detail about the value proposition of a business. On what proposition must a businessman position his product ( Performance value, Relational Value, Emotional value, Relationship Value ). Next, he outlines how to deliver the selected product to the selected customer through an effective marketing communication strategy, value packaging and positioning mechanism, and the right communication channel. This video package is a powerful solution towards upgrading a start up business
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Dr. Vivek Bindra: Motivational Speaker

Defining and understanding what it means to take the product of a matrix and a vector
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/introduction-to-the-null-space-of-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Khan Academy

Given some matrices, in what order you would multiply them to minimize cost of multiplication.
https://github.com/mission-peace/interview/blob/master/src/com/interview/dynamic/MatrixMultiplicationCost.java

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Tushar Roy - Coding Made Simple

This video explains how to write a matrix as a product of elementary matrices.
Site: mathispower4u.com
Blog: mathispower4u.wordpress.com

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Mathispower4u

Elementary row or column operations on a matrix does not change the nature of the matrix. There are three elementary operations possible on a matrix
Row or column interchange. Multiplying all elements of a row or column by a non zero number. Adding a non zero multiple of corresponding elements of another row or column to the elements of a row or column.

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MathsSmart

100% innovative way for product of two Matrix. Please consider a11 element in Q.1 as 2 not zero.

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Anshuman Purohit

Follow @mathbff on Instagram, Facebook and Twitter!

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mathbff

Today;s Topic is :- Product of Matrix class -7 | Business Mathematics | Excercise solved | By free ki pathshala
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Matrices shortcuts and tricks
Multiplication of matrices
tricks to multiply matrices
matrix multiplication
Class 11 matrices
class 12 matrices
Matrices multiplication inverse 3x3 2x2 3x2
Unit II: Algebra
1. Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists;
2. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
Introduction and Examples
DEFINITION: A matrix is defined as an ordered rectangular array of numbers. They can be used to represent systems of linear equations, as will be explained below.
Here are a couple of examples of different types of matrices:
Symmetric Diagonal Upper Triangular Lower Triangular Zero Identity
Symmetric Matix Diagonal Matrix Upper Triangular Matix Lower Triangular Matix Zero Matix Identity Matix
And a fully expanded m×n matrix A, would look like this:
n×n matrix
... or in a more compact form: m×n simplified
Top
Matrix Addition and Subtraction
DEFINITION: Two matrices A and B can be added or subtracted if and only if their dimensions are the same (i.e. both matrices have the same number of rows and columns. Take:
matrices A&B
Addition
If A and B above are matrices of the same type then the sum is found by adding the corresponding elements aij + bij .
Here is an example of adding A and B together.
Sum of matrices A&B
Subtraction
If A and B are matrices of the same type then the subtraction is found by subtracting the corresponding elements aij − bij.
Here is an example of subtracting matrices.
Subtraction of A&B
Now, try adding and subtracting your own matrices.
Addition/subtraction Top
Matrix Multiplication
DEFINITION: When the number of columns of the first matrix is the same as the number of rows in the second matrix then matrix multiplication can be performed.
Here is an example of matrix multiplication for two 2×2 matrices.
Matrix multiplication 2×2
Here is an example of matrix multiplication for two 3×3 matrices.
Matrix multiplication 3×3
Now lets look at the n×n matrix case, Where A has dimensions m×n, B has dimensions n×p. Then the product of A and B is the matrix C, which has dimensions m×p. The ijth element of matrix C is found by multiplying the entries of the ith row of A with the corresponding entries in the jth column of B and summing the n terms. The elements of C are:
Matrix multiplication for n×n
Note: That A×B is not the same as B×A
Now, try multiplying your own matrices.
Matrix multiplication Top
Transpose of Matrices
DEFINITION: The transpose of a matrix is found by exchanging rows for columns i.e. Matrix A = (aij) and the transpose of A is:
AT = (aji) where j is the column number and i is the row number of matrix A.
For example, the transpose of a matrix would be:
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Free Ki Pathshala

Hello friends I'm starting a playlist to help you all to do some most common as well as rare programs of c++.
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Geek n Tech Hindi

I discuss element by element matrix operations such as element by element addition, element by element subtraction, element by element multiplication (the dot product), element by element division. Then I go on to discuss matrix multiplication and matrix division. I try to give examples of objects opposed to just a matrix of numbers (like often seen in mathematics classes) to help beginners conceptualise the concepts.

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Philip Yip

Introduction to the concept of a matrix. Identify elements in a matrix.

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Sherry Holcomb

Inverse of 3x3 matrix example. Visit http://Mathmeeting.com to see all all video tutorials covering the inverse of a 3x3 matrix.

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Math Meeting

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For this problem you are given a matrix with an unknown element in it and then to find the value that makes the matrix singular i.e. $$\det{(A)}=0$$ you just use the determinant to create a polynomial and then solve for the unknown.

Views: 14220
JJtheTutor

Review the basics of the price component of the marketing mix. This critical element of your marketing strategy can make or break your competitive position. Provided by Rasmussen College School of Business.Download the PowerPoint presentation at http://www.sophia.org/marketing-mix-pricing-basics-tutorial

Views: 227809
Soma Datta

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/e/multiplying_a_matrix_by_a_vector?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Watch the next lesson: https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/v/defined-and-undefined-matrix-operations?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Khan Academy

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

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MathTheBeautiful

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
The individual items in an m × n matrix A, often denoted by ai,j, where max i = m and max j = n, are called its elements or entries.[4] Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be added or subtracted element by element (see Conformable matrix). The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second (i.e., the inner dimensions are the same, n for Am,n × Bn,p). Any matrix can be multiplied element-wise by a scalar from its associated field. A major application of matrices is to represent linear transformations, that is, generalizations of linear functions such as f(x) = 4x. For example, the rotationof vectors in three-dimensional space is a linear transformation, which can be represented by a rotation matrix R: if v is a column vector (a matrix with only one column) describing the position of a point in space, the product Rv is a column vector describing the position of that point after a rotation. The product of two transformation matrices is a matrix that represents the composition of two transformations. Another application of matrices is in the solution of systems of linear equations. If the matrix is square, it is possible to deduce some of its properties by computing its determinant. For example, a square matrix has an inverse if and only ifits determinant is not zero. Insight into the geometryof a linear transformation is obtainable (along with other information) from the matrix's eigenvalues and eigenvectors.

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Shiva Classes

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Marketing is everything involved in creating, communicating, and delivering value to customers, clients, and even society. Marketing is involved in everything from the market research that goes into determining what products consumers are looking for, to the message that is transmitted to consumers to inform them about a product and even persuade them to purchase it. In between those stages, marketing also plays a prominent role in determining how the product should look, designing the packaging that will enclose the product, deciding whether to sell the product through traditional retailers or entirely online, and establishing a price point that is not only attractive to consumers but allows gives the business the opportunity to be profitable.
Now when most people think of marketing they often think of advertising, which is completely understandable given we are are constantly exposed to advertisements at home, at the office, and even during our commutes. Although advertising is a component of marketing it certainly does not explain the entire subject. In fact, advertising is simply one of the four different types of promotion, and promotion is one of the four main elements of marketing. So you can see that advertising, like the other marketing elements, merely plays a role in helping businesses create, communicate, and deliver a single unified message to potential customers.
So how does a businesses create, communicate, and deliver value to its customers? Although there are many variables at work, a business can increase the probability of success by creating an effective and consistent marketing mix. Often referred to as the 4 P's, the market mix is a collection of four elements that outline the strategy for how a business intends to reach its customers. These four elements include product, place, promotion, and price.
The product includes the tangible product or intangible service that will be used to fulfill a customer need or want. The features of a product, its physical form, packaging, warranties, and even after-sale service are all included under the product strategy.
Place includes how a business intends to get products from the location they are produced to where they can ultimately be consumed by consumers. Place is often referred to as distribution since we are dealing with logistics. However, place not only includes the physical distribution of the product but also the channel through which it will be sold.
Promotion involves establishing the most effective method for communicating with its customers about the various products that it sells. Promotion is primarily meant to communicate, inform, and persuade. An effective promotion strategy, like the other marketing mix elements, depends upon a businesses knowledge of its target customer. This knowledge allows a business to select the best way to communicate with its core audience and ultimately increase the success of its communications.
The last element of the market mix is price. Price is the easiest marketing mix element to alter from a technical sense, however it is the most difficult thing to change. The reason is that altering the price of a product affects what consumers pay for that product, and a business can only charge as much as the market is willing to pay for a product. Technically a business can charge whatever price it wants, but that does not mean that consumers have to pay that price. Like the other marketing mix elements, price can send a message to consumers. For example, many believe that maintaining low prices is the best method to attract consumers. Although this can be an effective pricing strategy for certain items, it can also confuse consumers. For example, Tiffany & Co. sells expensive jewelry and is known for high quality and is one of the most recognizable brands. Because Tiffany & Co is known for quality and maybe even exclusivity, it wouldn't benefit from a low price point. Dealing with the psychological aspect of pricing, consumers tend to view less expensive items as cheap in quality compared to their more expensive counterparts. Although this doesn't always hold to be true, businesses are very aware of the impact that price can have on the perceptions of consumers.

Views: 49768
Alanis Business Academy

🌎 Brought to you by: https://StudyForce.com
🤔 Still stuck in math? Visit https://StudyForce.com/index.php?board=33.0 to start asking questions.
Conformable matrices: The product of \mathbf{AB} of two matrices A and B is defined only when the number of columns in matrix A equals the number of rows in matrix B.
Q. Given the matrices: (Difficulty: Easy)
Find the product of A•B.
Tip: The dimension of the resultant matrix will always have the # of rows of the first matrix and the # of columns of the second matrix.
*Definition of Matrix Multiplication*
The product of an m × n matrix, A, and an n × p matrix, B, is an m × p matrix, AB, whose elements are found as follows: The element in the ith row and jth column of AB is found by multiplying each element in the ith row of A by the corresponding element in the jth column of B and adding the products.
For the product of two matrices to be defined, the number of columns of the first matrix must equal the number of rows of the second matrix.
*Properties of Matrix Multiplication*
If A, B, and C are matrices and c is a scalar, then the following properties are true. (Assume the order of each matrix is such that all operations in these properties are defined.)
1. (AB)C = A(BC) Associative property of matrix multiplication
2. A(B + C) = AB + AC Distributive properties of matrix
(A + B)C = AC + BC multiplication
3. c(AB) = (cA)B Associative property of scalar multiplication.

Views: 32
Study Force

Gernot Akemann
Universität Bielefeld
March 19, 2014
For more videos, visit http://video.ias.edu

Views: 156
Institute for Advanced Study

In this video You know about matrix representation of various symmetry elements by Prof.Miss.Ranjana Kaushik.
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My other videos-
symmetry element part 1-https://youtu.be/XrhtL-usIfc
Symmetry element part 2-https://youtu.be/pcAAecdbeYQ
Molecular point group-https://youtu.be/3W9KAPRUVEU
Group postulates-https://youtu.be/0fIkccLGRMg
C2V multiplication table-https://youtu.be/bq6HGUGa0Fo
sub group and class-https://youtu.be/ia30anPKxo8
matrix representation-https://youtu.be/YDskYqE80Mc

Views: 30028
Ranjana kaushik Chemistry

http://www.tvchoice.uk.com - 31 mins, 2013
Key Topics
Value Analysis
Product Life Cycle
Product Portfolio
Boston Matrix
Product Differentiation
Brand Extension/Product Extension
An exploration of what most marketers would regard as the most important element of the Marketing Mix: Product.
PART 1 (15 mins): All About The Marketing Mix: Product. An introduction into the essentials of "product". What is value analysis? How is it done? What is the product life cycle? How can a business extend the life of a product? What is meant by brand extension? Also includes the Boston Matrix as a way of analysing a product portfolio.
PART 2 (8 mins): Case Studies In Value Analysis. Apple iPad compared to the Panasonic Toughpad. Tesco's Everyday Value range.
PART 3 (8 mins): Cash Cows, Stars & Dogs: Coca Cola is the cash cow that has funded new products, including "dogs" such as New Coke and Dasani in UK. Apple's come-back cash cow was the iPod, but that has been superseded by iPhone and iPad. McCain Foods' Oven Chips are the cash cow that has funded many variants.
TV CHOICE has a range of over 200 educational films and film clips for Business Studies, Geography, History, Leisure and Tourism and many other subjects. USA FORMATS AVAILABLE. http://www.tvchoice.uk.com

Views: 2095
TVChoiceFilms

Let's now try to define the multiplication of two square matrices of the same size. The only requirement we would like this definition to satisfy is that their product should transform any vector the same way as two consecutive transformations by one and then another matrix. In other words, multiplication of matrices is equivalent to composition of transformations they represent.
This can be expressed as
(A·B)·u = A·(B·u)
In the two-dimensional case this requirement results in the following chain of logical conclusions.
If
matrix A=[aij], i,j ∈ [1,2]
matrix B=[bij], i,j ∈ [1,2]
matrix C=A·B=[cij], i,j ∈ [1,2]
vector u=(u1,u2)
vector v=B·u=(v1,v2)
vector w=A·v=A·(B·u)=(w1,w2)
then:
(1) the transformation v=B·u looks like
v1 = b11·u1+b12·u2
v2 = b21·u1+b22·u2
(2) the transformation w=A·v looks like
w1 = a11·v1+a12·v2 =
= a11·(b11·u1+b12·u2) +
+ a12·(b21·u1+b22·u2) =
= (a11·b11+a12·b21)·u1 +
+ (a11·b12+a12·b22)·u2
w2 = a21·v1+a22·v2 =
= a21·(b11·u1+b12·u2) +
+ a22·(b21·u1+b22·u2) =
= (a21·b11+a22·b21)·u1 +
+ (a21·b12+a22·b22)·u2
Since we want to define a matrix product C=A·B=[cij] to perform the same transformation as a composition of, first, B and then A, as derived above, the same vector w should result from a multiplication of matrix C by vector u, that is
w1 = c11·u1+c12·u2
w2 = c21·u1+c22·u2
Comparing this with the derivation above, we conclude:
c11 = a11·b11+a12·b21
c12 = a11·b12+a12·b22
c21 = a21·b11+a22·b21
c22 = a21·b12+a22·b22
The above is a definition of a product of two 2x2 matrices C=A·B that satisfies our requirement of representing a transformation C equivalent to a composition of transformations of these two matrices, first, B and then A.
As you see, we have derived this definition based on a reasonable assumption about its properties.
Looking at these expressions above, we can notice that the ij-th element of matrix C is a scalar product of two vectors: i-th row-vector of matrix A, denoted as Ai or ai*=(ai1,ai2), and j-th column-vector of matrix B, denoted as B j or b*j=(b1j,b2j).

Views: 357
Zor Shekhtman

In order to find the inverse of a 3x3 matrix you need to be able to calculate the cofactor matrix based on the minors of each element. In this tutorial I show you how this is done.
Go to http://www.examsolutions.net/ for the index, playlists and more maths videos on exam solutions and other maths topics.

Views: 2904
ExamSolutions

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Marc Sylvester

We can compute the matrix elements of any operator (relative to an orthonormal basis) using inner products. This video shows how.

Views: 1227
Lorenzo Sadun

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A Trick to & How to find the INVERSE of a 3x3 Matrix, this is shortcut method to find inverse. this is best alternative to Gauss -Jordan or Row Column Transformation method. Useful for CBSE NCERT class 12. And calculus . Inverse of matrices 3x3 & 2x2 . elementary operation transformation is Already Explained in HINDI on my channel.Matrices in imp topic for CBSE(NCERT) class 12 .You can also find it useful for NCERT Solution.
tricks of matrices are also useful in JEE and CET.
Matrices and Determinants in Most imp. Chapter for class 12 .
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Mandhan Academy

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