Example
Solve the following system of linear equations by using Matrix Inversion Rule: 2x – y + 3z = 8, – x + 2y + z = 4 and 3x + y – 4z = 0.
Sol:
The given system of linear equations can be written in the form of AX = B, where
Now, det(A)
=
=
2(– 9) + 1(1) + 3(– 7)
=
– 18 + 1 – 21 = – 38
∴ Δ
=
– 38 ≠ 0
A is a non-singular matrix, A
– 1
exist.
Hence, we can solve the given system of equations by matrix inversion method.
Adj(A)
=
(cofactors of A)
T
=
From matrix inversion method, X
=
A
– 1
B
∴ The solution is x = y = z = 2.