Question 655566

№	X1	X2	X3	b
1	1	4	-3	-8
2	3	-1	3	12
3	1	1	6	1

Write down the main matrix and find its determinant


№	X1	X2	X3
1	1	4	-3
2	3	-1	3
3	1	1	6

D=-81

Replace the 1st column of the main matrix with the solution vector and find its determinant

№	X1	X2	X3
1	-8	4	-3
2	12	-1	3
3	1	1	6

D1=-243

Replace the 2nd column of the main matrix with the solution vector and find its determinant

№	X1	X2	X3
1	1	-8	-3
2	3	12	3
3	1	1	6

D2=216

Replace the 3rd column of the main matrix with the solution vector and find its determinant

№	X1	X2	X3
1	1	4	-8
2	3	-1	12
3	1	1	1

D3=-9

Solution set:
x1 = D1 / D = -243 / (-81) = 3

x2 = D2 / D = 216 / (-81) = -8/3

x3 = D3 / D = -9 / (-81) = 1/9