Explanation Given Information: There are three matrixes given as A = [ 1 2 0 3 ] , B = [ 3 − 2 4 5 ] , and C = [ 1 6 2 0 ] . Formula Used: Distributive law: Multiplying the matrix C on the right by the two matrices, A and B which are added together is same as performing each multiplication separately, that is, A C and B C , then adding. The property is as follows: ( A + B ) C = A C + B C Proof: Consider the given matrices, A = [ 1 2 0 3 ] , B = [ 3 − 2 4 5 ] , C = [ 1 6 2 0 ] Apply the distributive law on the matrices as follows: First compute the left side of the property that is ( A + B ) C . Add the corresponding entries of the two matrices A and B . A + B = [ 1 2 0 3 ] + [ 3 − 2 4 5 ] = [ 1 + 3 2 + ( − 2 ) 0 + 4 3 + 5 ] = [ 4 0 4 8 ] Now, multiply the resultant matrix by the matrix C . ( A + B ) C = [ 4 0 4 8 ] [ 1 6 2 0 ] = [ 4 ⋅ 1 + 0 ⋅ 2 4 ⋅ 6 + 0 ⋅ 0 4 ⋅ 1 + 8 ⋅ 2 4 ⋅ 6 + 8 ⋅ 0 ] = [ 4 + 0 24 + 0 4 + 16 24 + 0 ] = [ 4 24 20 24 ] Now, compute the right side of the property that is A C + B C

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 2.3, Problem 61E

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To prove: The distributive law for the matrices A=[1203], B=[3−245], and C=[1620].

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Chapter 2.3, Problem 60E

Chapter 2.3, Problem 62E

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To prove: The distributive law for the matrices A = [ 1 2 0 3 ] , B = [ 3 − 2 4 5 ] , and C = [ 1 6 2 0 ] .

Solution Summary: The author explains how to prove the distributive law for the matrices A, B, and C.

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To prove: The distributive law for the matrices A=[1203], B=[3−245], and C=[1620].

Want to see the full answer?

Chapter 2 Solutions