Question

Solve the system of linear equations using the Gauss-Jordan elimination method.

2x	+	2y	+	z	=	3
x			+	z	=	2
		4y	−	3z	=	13

solve for x,y,x

Answer 1

matrix

	X1	X2	X3	b
1	2	2	1	3
2	1	0	1	2
3	4	0	-3	13

Write the main matrix

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

Determinant is not zero, therefore inverse matrix exists

matrix

	A1	A2	A3
1	2	2	1
2	1	0	1
3	4	0	-3

Determinant is not zero, therefore inverse matrix exists

Write the augmented matrix

	A1	A2	A3	B1	B2	B3
1	2	2	1	1	0	0
2	1	0	1	0	1	0
3	4	0	-3	0	0	1

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

	A1	A2	A3	B1	B2	B3
1	1	0	1	0	1	0
2	2	2	1	1	0	0
3	4	0	-3	0	0	1

Eliminate the 1st column

	A1	A2	A3	B1	B2	B3
1	1	0	1	0	1	0
2	0	2	-1	1	-2	0
3	0	0	-7	0	-4	1

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

	A1	A2	A3	B1	B2	B3
1	1	0	1	0	1	0
2	0	1	-1/2	1/2	-1	0
3	0	0	-7	0	-4	1

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

	A1	A2	A3	B1	B2	B3
1	1	0	1	0	1	0
2	0	1	-1/2	1/2	-1	0
3	0	0	1	0	4/7	-1/7

Eliminate the 3rd column

	A1	A2	A3	B1	B2	B3
1	1	0	0	0	3/7	1/7
2	0	1	0	1/2	-5/7	-1/14
3	0	0	1	0	4/7	-1/7

There is the inverse matrix on the right

	A1	A2	A3	B1	B2	B3
1	1	0	0	0	3/7	1/7
2	0	1	0	1/2	-5/7	-1/14
3	0	0	1	0	4/7	-1/7

inverse matrix

	X1	X2	X3
1	0	3/7	1/7
2	1/2	-5/7	-1/14
3	0	4/7	-1/7

Multiply the inverse matrix by the solution vector

	X
1	19/7
2	-6/7
3	-5/7

Solution set:

x1 = 19/7

x2 = -6/7

x3 = -5/7

please like ??