Explanation Approach: A system of linear equations can be written in the form of A X = B where A is called the coefficient matrix, B is called the known matrix, and X is called the variable matrix. If a square matrix A of dimension 3 × 3 has an inverse A − 1 , and if X is a variable matrix and B is a known matrix both with n rows, then the solution of the matrix equation A X = B is given as follows. X = A − 1 B . Take a 3 × 6 matrix with left half as matrix B and right half as I 3 and transform the left half into identity matrix by performing elementary row operations on the entire matrix, the right half becomes inverse of the matrix B . Calculation: The given system of linear equations { 5 x + 7 y + 4 z = 1 3 x − y + 3 z = 1 6 x + 7 y + 5 z = 1 can be written as a single matrix equation A X = B as follows. [ 5 7 4 3 − 1 3 6 7 5 ] [ x y z ] = [ 1 1 1 ] Here, A = [ 5 7 4 3 − 1 3 6 7 5 ] , B = [ 1 1 1 ] , and X = [ x y z ] . The solution of this matrix equation is given by X = A − 1 B . First, find A − 1 , Take a matrix of dimension 3 × 6 with left half as matrix A and right half as I 3 and perform row operations to transform the left half into I 3 . [ 5 7 4 1 0 0 3 − 1 3 0 1 0 6 7 5 0 0 1 ] R 1 → 1 5 R 1 → [ 1 7 5 4 5 1 5 0 0 3 − 1 3 0 1 0 6 7 5 0 0 1 ] R 2 → R 2 − 3 R 1 → [ 1 7 5 4 5 1 5 0 0 0 − 26 5 3 5 − 3 5 1 0 6 7 5 0 0 1 ] R 3 → R 3 − 6 R 1 → [ 1 7 5 4 5 1 5 0 0 0 − 26 5 3 5 − 3 5 1 0 0 − 7 5 1 5 − 6 5 0 1 ] R 2 → − 5 26 R 2 → [ 1 7 5 4 5 1 5 0 0 0 1 − 3 26 3 26 − 5 26 0 0 − 7 5 1 5 − 6 5 0 1 ] R 3 → R 3 + 7 5 R 2 → [ 1 7 5 4 5 </

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 11.3, Problem 44E

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The system of equations {5x+7y+4z=13x−y+3z=16x+7y+5z=1 by converting it into a matrix equation and find the values of x, y and z.

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Chapter 11.3, Problem 43E

Chapter 11.3, Problem 45E

Chapter 11 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The system of equations { 5 x + 7 y + 4 z = 1 3 x − y + 3 z = 1 6 x + 7 y + 5 z = 1 by converting it into a matrix equation and find the values of x , y and z .

Solution Summary: The author explains how a system of linear equations can be written in the form of AX=B.

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To solve:

The system of equations {5x+7y+4z=13x−y+3z=16x+7y+5z=1 by converting it into a matrix equation and find the values of x, y and z.

Want to see the full answer?

Chapter 11 Solutions

The system of equations { 5 x + 7 y + 4 z = 1 3 x − y + 3 z = 1 6 x + 7 y + 5 z = 1 by converting it into a matrix equation and find the values of x , y and z .

Solution Summary: The author explains how a system of linear equations can be written in the form of AX=B.

Videos

To solve: The system of equations {5x+7y+4z=13x−y+3z=16x+7y+5z=1 by converting it into a matrix equation and find the values of x, y and z.

Want to see the full answer?

Chapter 11 Solutions

To solve:

The system of equations {5x+7y+4z=13x−y+3z=16x+7y+5z=1 by converting it into a matrix equation and find the values of x, y and z.