Explanation Given information: The matrix equation is [ 1 − 2 7 5 − 1 6 3 4 − 8 ] [ x y z ] = [ 9 − 4 2 ] . Formula used: 1) Definition: Matrix multiplication The product of m × n matrix A over ℝ and n × p matrix B over ℝ is m × p matrix C = A B , where the element c i j in row i and column j of A B is found by using the elements in row i of A , and the elements in column j of B in the following manner: c o l u m n j o f B c o l u m n j o f C r o w i o f A [ ⋮ ⋮ ⋮ ⋮ a i 1 a i 2 a i 3 ⋯ a i n ⋮ ⋮ ⋮ ⋮ ] ⋅ [ ⋯ b 1 j ⋯ ⋯ b 2 j ⋯ ⋯ b 3 j ⋯ ⋮ ⋯ b n j ⋯ ] = [ ⋮ ⋯ c i j ⋯ ⋮ ] r o w i o f C Where c i j = a i 1 b 1 j + a i 2 b 2 j + ⋯ + a i n b n j . 2) Definition: Matrix Equality Two matrices A = [ a i j ] m × n and B = [ b i j ] p × q over a set S are equal if and only if m = p , n = q , and a i j = b i j for all pairs of i , j

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ISBN: 9781285463230

Author: Gilbert, Linda, Jimmie

Publisher: Cengage Learning,

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Chapter 1.6, Problem 5E

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To prove: The matrix equation [1−2 75−1 63 4−8][xyz]=[ 9−4 2] is equivalent to a system of linear equations in x, y, and z.

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Chapter 1.6, Problem 4E

Chapter 1.6, Problem 6E

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To prove: The matrix equation [ 1 − 2 7 5 − 1 6 3 4 − 8 ] [ x y z ] = [ 9 − 4 2 ] is equivalent to a system of linear equations in x , y , and z .

Solution Summary: The author explains how the matrix equation is equivalent to a system of linear equations in x,y, and

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To prove: The matrix equation [1−2 75−1 63 4−8][xyz]=[ 9−4 2] is equivalent to a system of linear equations in x, y, and z.

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Chapter 1 Solutions