Question

4. Solve the system of equations.

2x – y + z = –7

x – 3y + 4z = –19

–x + 4y – 3z = 18.

    

A. There is one solution (–1, –2, –3).

B. There is one solution (1, 2, 3).

C. There is one solution (–1, 2, –3).

D. There is one solution (1, –2, 3).

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	2	-1	1	-7
2	1	-3	4	-19
3	-1	4	-3	18

Find the pivot in the 1st column and swap the 2nd and the 1st rows

	X1	X2	X3	b
1	1	-3	4	-19
2	2	-1	1	-7
3	-1	4	-3	18

Eliminate the 1st column

	X1	X2	X3	b
1	1	-3	4	-19
2	0	5	-7	31
3	0	1	1	-1

Find the pivot in the 2nd column and swap the 3rd and the 2nd rows

	X1	X2	X3	b
1	1	-3	4	-19
2	0	1	1	-1
3	0	5	-7	31

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	7	-22
2	0	1	1	-1
3	0	0	-12	36

Make the pivot in the 3rd column by dividing the 3rd row by -12

	X1	X2	X3	b
1	1	0	7	-22
2	0	1	1	-1
3	0	0	1	-3

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	-1
2	0	1	0	2
3	0	0	1	-3

Solution set:

x = -1

y = 2

z = -3

C. There is one solution (–1, 2, –3).