Question

Find the complete solution by reducing the augmented matrix to row-echelon form and show all the matrices, using arrows to indicate the order

x-2y+z= -3

2x-7y+8z= -12

3x-2y-5z= -1

Answer 1

reducing the augmented matrix to row-echelon form

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	X3	b
1	1	-2	1	-3
2	2	-7	8	-12
3	3	-2	-5	-1

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

	X1	X2	X3	b
1	1	-2	1	-3
2	2	-7	8	-12
3	3	-2	-5	-1

Eliminate the 1st column

	X1	X2	X3	b
1	1	-2	1	-3
2	0	-3	6	-6
3	0	4	-8	8

Make the pivot in the 2nd column by dividing the 2nd row by -3

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

Eliminate the 2nd column

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

Solution set:

x = 1 + 3z

y = 2 + 2z

z - free