Question

Using the Gauss-Jordan Method find the inverse of the matrix

[5 -2

6 2]

Answer 1

Using the Gauss-Jordan Method find the inverse of the matrix

[5 -2

6 2]

solution

Your matrix

	A1	A2
1	5	-2
2	6	2

Determinant is not zero, therefore inverse matrix exists

Write the augmented matrix

	A1	A2	B1	B2
1	5	-2	1	0
2	6	2	0	1

Make the pivot in the 1st column by dividing the 1st row by 5

	A1	A2	B1	B2
1	1	-2/5	1/5	0
2	6	2	0	1

Eliminate the 1st column

	A1	A2	B1	B2
1	1	-2/5	1/5	0
2	0	22/5	-6/5	1

Make the pivot in the 2nd column by dividing the 2nd row by 22/5

	A1	A2	B1	B2
1	1	-2/5	1/5	0
2	0	1	-3/11	5/22

Eliminate the 2nd column

	A1	A2	B1	B2
1	1	0	1/11	1/11
2	0	1	-3/11	5/22

There is the inverse matrix on the right

	A1	A2	B1	B2
1	1	0	1/11	1/11
2	0	1	-3/11	5/22

Result:

	B1	B2
1	1/11	1/11
2	-3/11	5/22