   Chapter 11.1, Problem 61E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS 4 9 - 6 4 ■ Solving a Linear Systems Solve the system of linear equations. { x −   y         + w = 0 3 x         − z   + 2 w = 0 x − 4 y + z + 2 w = 0

To determine

To solve:

The system of a linear equations.

Explanation

Given:

The system of linear equations is,

{xy+w=03xz+2w=0x4y+z+2w=0

Approach:

Write the augmented matrix of the system.

Use elementary row operations to change the augmented matrix to row-echelon form.

Write the new system of equations that corresponds to the row-echelon form of the augmented matrix and solve by back-substitution.

Calculation:

Consider the system of equations {xy+w=03xz+2w=0x4y+z+2w=0.

The augmented matrix is given by,



Transform the augmented matrix into row echelon form.

Perform the transformation R1R23R1.

[1101033(1)03(1)13(0)23(1)03(0)14120]

Perform the transformation R3R3R1.

[1101003110114(1)1(0)2(1)00]

Perform the transformation R2R23

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