   Chapter 11.1, Problem 32E ### 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

# 2 9 - 3 8 Linear Systems with One Solution The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. { x + y + z = 4 − x + 2 y + 3 z = 17 2 x − y          = − 7

To determine

To solve:

The system of equations {x+y+z=4x+2y+3z=172xy        =7 using Gauss-Jordan elimination.

Explanation

Procedure:

For solving the system of equations the following steps are required:

1. Write the augmented matrix of the system.

2. Perform the elementary row operation to change the augmented matrix to row-echelon form.

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

Calculation:

Consider the system of equations {x+y+z=4x+2y+3z=172xy        =7.

The augmented matrix is .

Transform the augmented matrix into row echelon form.

Perform the transformation R2R2+R1.

[11141+12+13+117+42107]

Perform the transformation R3R32R1.

[11140342122(1)12(1)02(1)72(4)]

Perform the transformation R2R23.



Perform the transformation R3R3+3R2

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