matrices - Matrices and their properties A matrix is a...

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1 Matrices Properties, Operations, Algebra Matrices and their properties A matrix is a rectangular array of numbers; an atrix as ws and lumns m x n matrix has m rows and n columns If m = n we call it a square matrix A zero matrix is one which has zero entries everywhere Two matrices are equal if they have the same size and all their entries are equal Matrices and their properties Column matrix : is mx1 Row matrix : is 1 x n scalar multiple of a matrix : kA , where each entry is multiplied by k Operations on matrices: Addition/Subtraction Two matrices can be added or subtracted if they have the same size; A + B , A - B The result is obtained just by adding or subtracting individual entries
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2 Operations on matrices: Multiplication The product AB of two matrices is defined only if the left matrix, A , has the same number of columns as the right matrix, B , has rows m x r can multiply r x n to give m x n Note the order matters!! Operations on matrices: Multiplication If is an matrix, and B is an matrix, then the product = C is the matrix whose entries are determined as follows: to find the entry in row i , column j of single out from the matrix and from the matrix multiply together the corresponding entries from the w and column row and column add up the resulting products. Example: Product of 2 matrices A: 2 x 4, B: 4 x 7, C: 7 x 2 an give 9 potential products of which only 3 are can give 9 potential products, of which only 3 are defined Matrix multiplication example 121 231 133 143 112   
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3 Ex: 4143 124 , 0 1 3 1 260 2752 AB     Noncommutativity In general the products and BA are not equal. Verify it on a couple of 2 x 2 matrices Properties of Matrix Arithmetic (see text for complete list)
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matrices - Matrices and their properties A matrix is a...

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