Explanation Definition used: Product of Two Matrices: The product of an m × n matrix A and an n × k matrix B is the m × k matrix C = A B . The element in the i t h row and j t h column of matrix C has the form c i j = [ a i 1 a i 2 ⋯ a i n ] [ b 1 j b 2 j ⋮ b n j ] = [ a i 1 b 1 j + a i 2 b 2 j + ⋯ + a i n b n j ] Note that two matrices can be multiplied only if the number of columns in the first matrix is equal to the number of rows in the second. Calculation: The two matrices are A = [ a b c d e f ] and B = [ 1 2 3 4 5 6 ] . The products A B and B A are calculated as follows. Observe that the matrix product A B is defined; since the number of columns of A is equal to the number of rows of B . Use the definition of product of two matrices and obtained the matrix A B as follows. A B = [ a b c d e f ] ⋅ [ 1 2 3 4 5 6 ] = [ a ⋅ 1 + b ⋅ 3 + c ⋅ 5 a ⋅ 2 + b ⋅ 4 + c ⋅ 6 d ⋅ 1 + e ⋅ 3 + f ⋅ 5 d ⋅ 2 + e ⋅ 4 + f ⋅ 6 ] = [ a + 3 b + 5 c 2 a + 4 b + 6 c d + 3 e + 5 f 2 d + 4 e + 6 f ] Therefore, the products A B = [ a + 3 b + 5 c 2 a + 4 b + 6 c d + 3 e + 5 f 2 d + 4 e + 6 f ]

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

5th Edition

ISBN: 9780134179025

Author: Ronald J. Harshbarger, Lisa S. Yocco

Publisher: PEARSON

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Chapter 7.3, Problem 21E

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To find: The products AB and BA if A=[abcdef] and B=[123456].

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Chapter 7.3, Problem 20E

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Chapter 7 Solutions

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

Ch. 7.1 - In Exercises 14, solve the systems of equations....Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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The products A B and B A if A = [ a b c d e f ] and B = [ 1 2 3 4 5 6 ] .

Solution Summary: The author explains the product of two matrices: the mtimes n matrix A and the k matrix B.

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To find: The products AB and BA if A=[abcdef] and B=[123456].

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Chapter 7 Solutions