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Chapter 11: Q. 24 (page 793)

In Problems 20–25, solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

x−y+z=0x−y−5z−6=02x−2y+z−1=0

Short Answer

Expert verified

The solution isx,y,z|x=y+1,z=-1,yisanyrealnumber.

Step by step solution

01

Step 1. Given information

The given system of equations isx−y+z=0x−y−5z−6=02x−2y+z−1=0

02

Step 2. Solve system of equations using matrix

Write the augmented matrix that represents the system of equations

1−1101−1−562−211

Perform the operations R2=R2-R1,

1−1101−1−1−(−1)−5−(1)6−02−211→1−11000−662−211

Now, perform the operations R3=R3-2R1,

1−11000−662−2(1)−2−2(−1)1−2(1)1−2(0)→1−11000−6600−11

The system of equations corresponding to this matrix is

x-y+z=0-6z=6-z=1

So,

z=-1x-y+-1=0x-y=1x=y+1

Therefore, the solution isx,y,z|x=y+1,z=-1,yisanyrealnumber

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Most popular questions from this chapter

Graph each inequality by hand.

2x+y≥6

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility:

2x+3y≥62x+3y≤0

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

xy=1;y=2x+1

Graph the equation:y=3x+2

Graph the equation:y+4=x2
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