SOLUTION: Consider the circuit in the figure. The currents I1, I2, and I3 in amperes are given by the solution of the system of linear equations. 4I1 + 8I3 = 18 2I2 + 8I3 = 54

Your matrix

        X1	X2	X3	b
1	4	0	8	18
2	0	2	8	54
3	1	1	-1	0


Write down the main matrix and find its determinant

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

Δ = -56


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

        X1	X2	X3
1	18	0	8
2	54	2	8
3	0	1	-1

Δ1 = 252


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

        X1	X2	X3
1	4	18	8
2	0	54	8
3	1	0	-1

Δ2 = -504


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

        X1	X2	X3
1	4	0	18
2	0	2	54
3	1	1	0

Δ3 = -252


x1 = Δ1 / Δ = 252 / (-56) = -9/2
x2 = Δ2 / Δ = (-504) / (-56) = 9
x3 = Δ3 / Δ = (-252) / (-56) = 9/2


Solution set:

x1 = -9/2
x2 = 9
x3 = 9/2