Explanation The given matrices are A = [ 4 3 − 6 2 ] , B = [ 1 2 0 1 ] and C = [ 4 3 0 − 2 ] . The matrices A , B and C are 2 × 2 matrix and having same dimension. Obtain the product ( A × B ) × C , ( A × B ) × C = ( [ 4 3 − 6 2 ] [ 1 2 0 1 ] ) [ 4 3 0 − 2 ] = [ 4 ( 1 ) + 3 ( 0 ) 4 ( 2 ) + 3 ( 1 ) − 6 ( 1 ) + 2 ( 0 ) − 6 ( 2 ) + 2 ( 1 ) ] [ 4 3 0 − 2 ] = [ 4 + 0 8 + 3 − 6 + 0 − 12 + 2 ] [ 4 3 0 − 2 ] = [ 4 11 − 6 − 10 ] [ 4 3 0 − 2 ] On further simplification, obtain the matrix ( A × B ) × C , ( A × B ) × C = [ 4 11 − 6 − 10 ] [ 4 3 0 − 2 ] = [ 4 ( 4 ) + 11 ( 0 ) 4 ( 3 ) + 11 ( − 2 ) − 6 ( 4 ) − 10 ( 0 ) − 6 ( 3 ) − 10 ( − 2 ) ] = [ 16 + 0 12 − 22 − 24 − 0 − 18 + 20 ] = [ 16 − 10 − 24 2 ] Thus, the product of two matrices is ( A × B ) × C = [ 16 − 10

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Chapter 9.4, Problem 49E

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To show: The associative property of multiplication, (A×B)×C=A×(B×C) , where A=[43−62],B=[1201] and C=[430−2] .

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Chapter 9.4, Problem 48E

Chapter 9.4, Problem 50E

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The associative property of multiplication, ( A × B ) × C = A × ( B × C ) , where A = [ 4 3 − 6 2 ] , B = [ 1 2 0 1 ] and C = [ 4 3 0 − 2 ] .

Solution Summary: The author explains the associative property of multiplication. The matrices A, B and C are 2times 2 matrix and having same dimension.

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To show: The associative property of multiplication, (A×B)×C=A×(B×C) , where A=[43−62],B=[1201] and C=[430−2] .

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Chapter 9 Solutions