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Solve the system of simultaneous equations, using the method of determinants (Cramer’s Rule):
2x + y + z = 0
4x + 3y+ 2z = 2
2x - y -3z = 0
~~~~~~~~~~~~~~~~~
Solution
Your matrix
X1 X2 X3 b
1 2 1 1 0
2 4 3 2 2
3 2 -1 -3 0
Write down the main matrix and find its determinant
X1 X2 X3
1 2 1 1
2 4 3 2
3 2 -1 -3
Δ = -8
Replace the 1st column of the main matrix with the solution vector and find its determinant
X1 X2 X3
1 0 1 1
2 2 3 2
3 0 -1 -3
Δ1 = 4
Replace the 2nd column of the main matrix with the solution vector and find its determinant
X1 X2 X3
1 2 0 1
2 4 2 2
3 2 0 -3
Δ2 = -16
Replace the 3rd column of the main matrix with the solution vector and find its determinant
X1 X2 X3
1 2 1 0
2 4 3 2
3 2 -1 0
Δ3 = 8
x = Δ1 / Δ = 4 / (-8) = -1/2
y = Δ2 / Δ = (-16) / (-8) = 2
z = Δ3 / Δ = 8 / (-8) = -1
Solution set:
x = -1/2
y = 2
z = -1
Solved.
