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

2x+y-z=7

x+2y+z=8

x-2y+3z=2

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