undefined Solution The value of expressions ab , ba , aA , Bb . The value of expressions ab , ba , aA , Bb are [ 1 ] , [ 3 − 6 0 1 − 2 0 − 1 2 0 ] , [ 8 − 4 − 9 ] , [ 0 − 8 2 ] _ , respectively. Given: The matrices are A = [ 4 − 2 3 − 2 1 6 1 2 2 ] , B = [ 1 − 3 0 − 3 1 0 0 0 − 2 ] , C = [ 0 1 3 2 − 2 0 ] , a = [ 1 − 2 0 ] , b = [ 3 1 − 1 ] . Definition used: “Multiplication of matrices: The product C = AB (in this order) of an m × n matrix A = [ a j k ] times an r × p matrix B = [ b j k ] is defined if and only if r = n and is then the m × p matrix C = [ c j k ] with entries c j k = ∑ l = 1 n a j l b l k = a j 1 b 1 k + a j 2 b 2 k + ⋯ + a j n b n k , where j = 1 , 2 , … , m and k = 1 , 2 , … , p .” Transpose of a matrix: “The transpose of an m × n matrix A = a j k is the n × m matrix A T that has the first row of A as its first column , the second row of A as its second column , and so on. Thus the transpose of A is A T = [ a k j ] .” Calculation: The product of the matrix a and b is given by, ab = [ 1 − 2 0 ] [ 3 1 − 1 ] = [ 1 ( 3 ) + ( − 2 ) ( 1 ) + 0 ( − 1 ) ] = [ 3 − 2 ] = [ 1 ] The product of the matrix b and a is given by, ba = [ 3 1 − 1 ] [ 1 − 2 0 ] = [ 3 ( 1 ) 3 ( − 2 ) 3 ( 0 ) 1 ( 1 ) 1 ( − 2 ) 1 ( 0 ) − 1 ( 1 ) − 1 ( − 2 ) − 1 ( 0 ) ] = [ 3 − 6 0 1 − 2 0 − 1 2 0 ] The product of the matrix a and A is given by, aA = [ 1 − 2 0 ] [ 4 − 2 3 − 2 1 6 1 2 2 ] = [ 1 ( 4 ) + ( − 2 ) ( − 2 ) + 0 ( 1 ) 1 ( − 2 ) + ( 1 ) ( − 2 ) + 0 ( 2 ) 1 ( 3 ) + ( − 2 ) ( 6 ) + 0 ( 2 ) ] = [ 8 − 4 − 9 ] The product of the matrix B and b is given by, Bb = [ 1 − 3 0 − 3 1 0 0 0 − 2 ] [ 3 1 − 1 ] = [ 1 ( 3 ) + ( − 3 ) ( 1 ) + 0 ( 1 ) − 3 ( 3 ) + 1 ( 1 ) + 0 ( − 1 ) 0 ( 3 ) + 0 ( 1 ) + ( − 2 ) ( − 1 ) ] = [ 0 − 8 2 ] Thus, the value of expressions ab , ba , aA , Bb are [ 1 ] , [ 3 − 6 0 1 − 2 0 − 1 2 0 ] , [ 8 − 4 − 9 ] , [ 0 − 8 2 ] _ , respectively.

10th Edition

ISBN: 9781119664697

Author: Kreyszig

Publisher: WILEY

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