Question

solve the system of equations

x₁ + x₂ + x₃ = 7

x₁ - x₂ + 2x₃ = 7

5x₁ + x₂ + x₃ = 11

Answer 1

Augmented matrix fir the given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	1	1	1	7
2	1	-1	2	7
3	5	1	1	11

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

	X1	X2	X3	b
1	1	1	1	7
2	1	-1	2	7
3	5	1	1	11

Eliminate the 1st column

	X1	X2	X3	b
1	1	1	1	7
2	0	-2	1	0
3	0	-4	-4	-24

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

	X1	X2	X3	b
1	1	1	1	7
2	0	1	-1/2	0
3	0	-4	-4	-24

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	3/2	7
2	0	1	-1/2	0
3	0	0	-6	-24

Make the pivot in the 3rd column by dividing the 3rd row by -6

	X1	X2	X3	b
1	1	0	3/2	7
2	0	1	-1/2	0
3	0	0	1	4

Eliminate the 3rd column

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

Solution set:

x1 = 1

x2 = 2

x3 = 4