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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 m x n matrix has m rows and n columns m x n has 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 i d ll th i t i l size and all their entries are equal Matrices and their properties Column matrix : is m x 1 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 A is an m x r matrix, and B is an r x n matrix, then the product A B = C is the m x n matrix whose entries are determined as follows: to find the entry in row i , column j of AB single out row i from the matrix A and column j from the matrix B multiply together the corresponding entries from the 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 can give 9 potential products of which only 3 are can give 9 potential products, of which only 3 are defined Matrix multiplication example 1 2 1 2 3 1 1 3 3 1 4 3 1 1 2
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