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Unformatted text preview: If A and B are both m n matrices then the sum of A and B , denoted A + B , is a matrix obtained by adding corresponding elements of A and B .  = 3 1 2 2 1 A  = 4 1 2 4 3 B  = + 2 B A If A and B are both m n matrices then the sum of A and B , denoted A + B , is a matrix obtained by adding corresponding elements of A and B . add these  = 3 1 2 2 1 A  = 4 1 2 4 3 B  = + 2 2 B A add these  = 3 1 2 2 1 A  = 4 1 2 4 3 B  = + 6 2 2 B A add these  = 3 1 2 2 1 A  = 4 1 2 4 3 B  = + 2 6 2 2 B A add these  = 3 1 2 2 1 A  = 4 1 2 4 3 B  = + 2 6 2 2 B A add these  = 3 1 2 2 1 A  = 4 1 2 4 3 B  = + 1 2 6 2 2 B A add these A B B A + = + C B A C B A + + = + + ) ( ) ( If A is an m n matrix and s is a scalar, then we let kA denote the matrix obtained by multiplying every element of A by k. This procedure is called scalar multiplication. ( 29 ( 29 ( 29 ( 29 k hA kh A k h A kA hA k A B kA kB = + = + + = +  = 3 1 2 2 1 A ( 29 ( 29 ( 29 ( 29 ( 29 ( 29  =  = 9 3 6 6 3 3 3 1 3 3 2 3 2 3 1 3 3 A PROPERTIES OF SCALAR MULTIPLICATION The m n zero matrix , denoted , is the m n matrix whose elements are all zeros. ( 29 ) ( = = + = + A A A A A [ ] 2 2 1 3 The multiplication of matrices is easier shown than put into words. You multiply the rows of the first matrix with the columns of the second adding products  = 1 4 1 2 3 A  = 1 3 3 1 4 2 B Find AB First we multiply across the first row and down the...
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This note was uploaded on 01/12/2011 for the course MAT 116 A MAT 116 A taught by Professor Hawkins during the Spring '10 term at University of Phoenix.
 Spring '10
 HAWKINS

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