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 2 × 2 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 { 2 x + 4 y + z = 7 − x + y − z = 0 x + 4 y = − 2 can be written as a single matrix equation A X = B as follows: [ 2 4 1 − 1 1 − 1 1 4 0 ] [ x y z ] = [ 7 0 − 2 ] Here, A = [ 2 4 1 − 1 1 − 1 1 4 0 ] , B = [ 7 0 − 2 ] , and X = [ x y z ] . Now the solution of this matrix equation is given by X = A − 1 B . First, find A − 1 , Now we 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 . [ 2 4 1 1 0 0 − 1 1 − 1 0 1 0 1 4 0 0 0 1 ] R 1 ↔ R 3 → [ 1 4 0 0 0 1 − 1 1 − 1 0 1 0 2 4 1 1 0 0 ] R 2 → R 2 + R 1 → [ 1 4 0 0 0 1 0 5 − 1 0 1 1 2 4 1 1 0 0 ] R 3 → R 3 − 2 R 1 → [ 1 4 0 0 0 1 0 5 − 1 0 1 1 0 − 4 1 1 0 − 2 ] R 2 → 1 5 R 2 → [ 1 4 0 0 0 1 0 1 − 1 5 0 1 5 1 5 0 − 4 1 1 0 − 2 ] R 3 → R 3 + 4 R 2 → [ 1 4 0 0 0 1 0

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ISBN: 8220100548512

Author: Watson

Publisher: CENGAGE L

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Chapter 11.3, Problem 43E

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The system of equations {2x+4y+z=7−x+y−z=0x+4y=−2 by converting it into a matrix equation and find the values of x, y and z.

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Chapter 11.3, Problem 42E

Chapter 11.3, Problem 44E

Chapter 11 Solutions

EBK ALGEBRA AND TRIGONOMETRY

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 { 2 x + 4 y + z = 7 − x + y − z = 0 x + 4 y = − 2 by converting it into a matrix equation and find the values of x , y and z .

Solution Summary: The author explains how the system of linear equations c2x+4y+z=7 can be written as a single matrix equation AX=B.

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To solve:

The system of equations {2x+4y+z=7−x+y−z=0x+4y=−2 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 { 2 x + 4 y + z = 7 − x + y − z = 0 x + 4 y = − 2 by converting it into a matrix equation and find the values of x , y and z .

Solution Summary: The author explains how the system of linear equations c2x+4y+z=7 can be written as a single matrix equation AX=B.

Videos

To solve: The system of equations {2x+4y+z=7−x+y−z=0x+4y=−2 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 {2x+4y+z=7−x+y−z=0x+4y=−2 by converting it into a matrix equation and find the values of x, y and z.