   Chapter 11.1, Problem 45E ### 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

# 3 9 - 4 8 Dependent or Inconsistent Linear Systems Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. { x + 4 y − 2 z = − 3 2 x − y + 5 z = 12 8 x + 5 y + 11 z = 30

To determine

Whether the system of equation {x+4y2z=32xy+5z=128x+5y+11z=30 is inconsistent or dependent. If dependent, write the complete solution.

Explanation

Approach:

If the system of linear equations is not inconsistent and all the variable 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 {x+4y2z=32xy+5z=128x+5y+11z=30.

The augmented matrix is .

Transform the augmented matrix into row echelon form.

Perform the transformation R2R22R1.

[142322(1)12(4)52(2)122(3)851130]

Perform the transformation R3R38R1.

[14230991888(1)58(4)118(2)308(3)]

Perform the transformation R2R29

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