Question

1. Solve the following system of equations by the elimination method: 2x+y-z=7 x+2y+z=8 x-2y+3z=2 2. Solve...

1. Solve the following system of equations by the elimination method:

2x+y-z=7

x+2y+z=8

x-2y+3z=2

2. Solve the following system of equations by using row operations on a matrix:

2x+y-z=7

x+2y+z=8

x-2y+3z=2

Homework Answers

Answer #1

construct a marix

2 1 -1 7
1 2 1 8
1 -2 3 2

Divide row1 by 2

1 1/2 -1/2 7/2
1 2 1 8
1 -2 3 2


Add (-1 * row1) to row2

1 1/2 -1/2 7/2
0 3/2 3/2 9/2
1 -2 3 2


Add (-1 * row1) to row3

1 1/2 -1/2 7/2
0 3/2 3/2 9/2
0 -5/2 7/2 -3/2


Divide row2 by 3/2

1 1/2 -1/2 7/2
0 1 1 3
0 -5/2 7/2 -3/2


Add (5/2 * row2) to row3

1 1/2 -1/2 7/2
0 1 1 3
0 0 6 6


Divide row3 by 6

1 1/2 -1/2 7/2
0 1 1 3
0 0 1 1


Add (-1 * row3) to row2

1 1/2 -1/2 7/2
0 1 0 2
0 0 1 1


Add (1/2 * row3) to row1

1 1/2 0 4
0 1 0 2
0 0 1 1


Add (-1/2 * row2) to row1

1 0 0 3
0 1 0 2
0 0 1 1

solution is

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