SOLUTION: Use determinate method to solve 2x+3y-4z=-4 x-2y+2z=3 x+3y-2z=1

Your matrix

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


Write down the main matrix and find its determinant

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

Δ = -12


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

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

Δ1 = -12


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

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

Δ2 = -24


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

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

Δ3 = -36


x1 = Δ1 / Δ = (-12) / (-12) = 1
x2 = Δ2 / Δ = (-24) / (-12) = 2
x3 = Δ3 / Δ = (-36) / (-12) = 3


Solution set:

x1 = 1
x2 = 2
x3 = 3