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Chapter 11: Q. 52 (page 730)

In Problems 37鈥�72, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

2x-3y-z=0-x+2y+z=53x-4y-z=1

Short Answer

Expert verified

The system of equation is inconsistent.

Step by step solution

01

Step 1. Given information. 

The given system of equation are

2x-3y-z=0-x+2y+z=53x-4y-z=1

02

Step 2. Calculation. 

The augmented matrix of the system is:

2-3-1-1213-4-1051

Perform the row operations localid="1647508848641" R1=r1+2r2;R3=r3+3r2

011-12102210516

Perform the row operations R3=r3-2r1:

011-121000105-4

Use the obtained matrix to write the system of equations.

y+z=10-x+y+z=50=-4

This system is impossible to solve. Therefore, this system of equation is inconsistent.

03

Step 3. Conclusion. 

The system of equation is inconsistent.

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