   Chapter 11.1, Problem 51E ### 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. { 2 x + y + 3 z = 9 − x       − 7 z = 10 3 x + 2 y − z = 4

To determine

To solve:

The system of linear equations.

Explanation

Given:

The system of linear equations is,

{2x+y+3z=9x     7z=103x+2yz=4

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.

If the system of linear equations is not inconsistent and all the variables in the row-echelon form are not leading variables, then it has infinitely many solutions, and the system is called dependent.

If the row echelon form contains a row that represents the equation 0=c, then the system has no solution.

If the system of linear equations has no solutions, then it is inconsistent.

Calculation:

Consider the system of equations {2x+y+3z=9x     7z=103x+2yz=4

The augmented matrix is given by,



Transform the augmented matrix into row echelon form.

Perform the transformation R1R12.



Perform the transformation R2R2+R1.

[11232921+10+127+3210+923214]

Perform the transformation R3R33R1.

[112329201211229233(1)23(12)13(32)43(92)]

Perform the transformation R22R2

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