You can
put this solution on YOUR website! .
Your matrix
X1 X2 X3 X4 b
1 1 2 3 4 0
2 8 5 1 4 0
3 5 6 8 1 0
4 8 3 7 2 0
Write down the main matrix and find its determinant
X1 X2 X3 X4
1 1 2 3 4
2 8 5 1 4
3 5 6 8 1
4 8 3 7 2
Δ = -1034 <<<---=== Since the determinant is not zero, the solution to the system is the zero vector.
Explicit calculations below confirm this fact.
Replace the 1st column of the main matrix with the solution vector and find its determinant
X1 X2 X3 X4
1 0 2 3 4
2 0 5 1 4
3 0 6 8 1
4 0 3 7 2
Δ1 = 0
Replace the 2nd column of the main matrix with the solution vector and find its determinant
X1 X2 X3 X4
1 1 0 3 4
2 8 0 1 4
3 5 0 8 1
4 8 0 7 2
Δ2 = 0
Replace the 3rd column of the main matrix with the solution vector and find its determinant
X1 X2 X3 X4
1 1 2 0 4
2 8 5 0 4
3 5 6 0 1
4 8 3 0 2
Δ3 = 0
Replace the 4th column of the main matrix with the solution vector and find its determinant
X1 X2 X3 X4
1 1 2 3 0
2 8 5 1 0
3 5 6 8 0
4 8 3 7 0
Δ4 = 0
x1 = Δ1 / Δ = 0 / (-1034) = 0
x2 = Δ2 / Δ = 0 / (-1034) = 0
x3 = Δ3 / Δ = 0 / (-1034) = 0
x4 = Δ4 / Δ = 0 / (-1034) = 0
Solution set:
x1 = 0
x2 = 0
x3 = 0
x4 = 0
