2130_Chapter7_Notes

# Its not hard to see that every entry in the matrix 0

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Unformatted text preview: t two matrices must have the same dimensions in order to be equal. For example, 00 00 000 000 14 25 36 and 123 . 456 8 / 17 Scalar Multiplication & Matrix Addition The product of a matrix A aij and a constant k is deﬁned as kA in the matrix by the constant k. For example, A 12 34 The sum of two m ¢ n matrices A aij and B A 12 ,B 34 A B k ¤ aij ; i.e., simply multiply each entry ¡5 ¡10 . ¡15 ¡20 is deﬁned as A B ¡5A bij aij bij . For example, 56 78 1 5 2 6 3 7 4 8 68 . 10 12 9 / 17 5 Zero Matrix The zero matrix has the following property: A 0 A. It’s not hard to see that every entry in the matrix 0 is the number 0. The dimensions of the zero matrix depend on the context. All of the matrices below are zero matrices: 00 , 00 0 0 000 , 000 000 000. 000 0 Note that the zero matrix is not unique even though we use the same notation 0 for every zero matrix. 10 / 17 Matrix Multiplication The product of an m ¢ n matrix A cij Öaik × and an n ¢ p matrix B Öbkj × is deﬁned as AB n ô aik bkj ai1 b1j C Öcij ×, where ai2b2j ¤ ¤ ¤ ainbnj . k1 Note: if we deﬁ...
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## This note was uploaded on 03/19/2014 for the course APMA 2130 taught by Professor Bernardfulgham during the Fall '09 term at UVA.

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