Explanation Given Information: The provided matrix equation is: [ 1 − 1 4 − 1 3 − 3 1 3 3 0 1 ] [ x y z ] = [ − 3 − 1 2 ] Formula Used: Multiplication of Matrices: If A is an m × n matrix and B is an n × k matrix, then the product A B is the m × k matrix whose i j th entry is the product ( A B ) i j = [ a i 1 a i 2 a l i 3 ... a i n ] [ b 1 j b 2 j b 3 j . . . b n j ] = a i 1 b 1 j + a i 2 b 2 j + a i 3 b 3 j + ... + a i n b n j Calculation: Consider the provided matrix equation: [ 1 − 1 4 − 1 3 − 3 1 3 3 0 1 ] [ x y z ] = [ − 3 − 1 2 ] For calculating the corresponding matrix equation, first evaluate the left-side and then set it equal to the right-side. First, simplify the multiplication on the left-side: Here, A = [ 1 − 1 4 − 1 3 − 3 1 3 3 0 1 ] and B = [ x y z ]

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Chapter 4.2, Problem 46E

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To calculate: The translation of the matrix equation [1−14−13−313301][xyz]=[−3−12] into system of linear equations.

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Chapter 4.2, Problem 45E

Chapter 4.2, Problem 47E

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The translation of the matrix equation [ 1 − 1 4 − 1 3 − 3 1 3 3 0 1 ] [ x y z ] = [ − 3 − 1 2 ] into system of linear equations.

Solution Summary: The author calculates the translation of the matrix equation left[cc1& -1& 4 -

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To calculate: The translation of the matrix equation [1−14−13−313301][xyz]=[−3−12] into system of linear equations.

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Chapter 4 Solutions