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 = [ 1 − 1 2 3 4 4 ] and B = [ 3 1 1 3 − 2 1 ] . Observe that the number of columns of A is equal to the number of rows of B ; hence the matrix product A B is defined and has dimension 2 × 2 . Use the definition of product of two matrices and obtained the matrix product A B as follows. A B = [ 1 − 1 2 3 4 4 ] ⋅ [ 3 1 1 3 − 2 1 ] = [ 1 ⋅ 3 + ( − 1 ) ⋅ 1 + 2 ⋅ ( − 2 ) 1 ⋅ 1 + ( − 1 ) ⋅ 3 + 2 ⋅ 1 3 ⋅ 3 + 4 ⋅ 1 + 4 ⋅ ( − 2 ) 3 ⋅ 1 + 4 ⋅ 3 + 4 ⋅ 1 ] = [ 3 − 1 − 4 1 − 3 + 2 9 + 4 − 8 3 + 12 + 4 ] = [ − 2 0 5 19 ] Therefore, the product A B = [ − 2 0 5 19 ]

College Algebra in Context with Integrated Review and Worksheets Plus MyLab Math with Pearson eText-- Access Card Package

1st Edition

ISBN: 9780134380155

Author: Ronald J. Harshbarger, Lisa S. Yocco

Publisher: PEARSON

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Chapter 7.3, Problem 25E

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To compute: The products AB and BA, if A=[1−12344] and B=[3113−21].

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Chapter 7.3, Problem 24E

Chapter 7.3, Problem 26E

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Chapter 7 Solutions

College Algebra in Context with Integrated Review and Worksheets Plus MyLab Math with Pearson eText-- Access Card Package

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 = [ 1 − 1 2 3 4 4 ] and B = [ 3 1 1 3 − 2 1 ] .

Solution Summary: The author explains that two matrices can be multiplied only if the number of columns in the first matrix is the same.

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To compute: The products AB and BA, if A=[1−12344] and B=[3113−21].

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Chapter 7 Solutions