Question

The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss Jordan elimination. Show all your work.

x + y + z = 11

2x ? 3y + 2z = 7

4x + y ? 3z = 7

Answer 1

Augmented matrix for given system of equations

solution using Gaussian elimination or Gauss Jordan elimination

Your matrixt

	X1	X2	X3	b
1	1	1	1	11
2	2	-3	2	7
3	4	1	-3	7

Find the pivot in the 1st column in the 1st row

	X1	X2	X3	b
1	1	1	1	11
2	2	-3	2	7
3	4	1	-3	7

Eliminate the 1st column

	X1	X2	X3	b
1	1	1	1	11
2	0	-5	0	-15
3	0	-3	-7	-37

Make the pivot in the 2nd column by dividing the 2nd row by -5

	X1	X2	X3	b
1	1	1	1	11
2	0	1	0	3
3	0	-3	-7	-37

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	1	8
2	0	1	0	3
3	0	0	-7	-28

Make the pivot in the 3rd column by dividing the 3rd row by -7

	X1	X2	X3	b
1	1	0	1	8
2	0	1	0	3
3	0	0	1	4

Eliminate the 3rd column

	X1	X2	X3	b
1	1	0	0	4
2	0	1	0	3
3	0	0	1	4

Solution set:

x = 4

y = 3

z = 4