To determine The value of expressions 3 A − 2 B , ( 3 A − 2 B ) T , 3 A T − 2 B T , ( 3 A − 2 B ) T a T . Explanation 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: Use the definition transpose and find the transpose of 3 A − 2 B . 3 A − 2 B = 3 [ 4 − 2 3 − 2 1 6 1 2 2 ] − 2 [ 1 − 3 0 − 3 1 0 0 0 − 2 ] = [ 12 − 6 9 − 6 3 18 3 6 6 ] − [ 2 − 6 0 − 6 2 0 0 0 − 4 ] = [ 10 0 9 0 1 18 3 6 10 ] Use the above matrix, find the value of ( 3 A − 2 B ) T as follows

10th Edition

ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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Chapter 7.2, Problem 14P

To determine

The value of expressions 3A−2B,(3A−2B)T,3AT−2BT,(3A−2B)TaT.

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Chapter 7.2, Problem 13P

Chapter 7.2, Problem 15P

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Advanced Engineering Mathematics

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