Given system of equations is:

3x + 2y – 2z = 3,

x + 2y + 3z = 6,

2x – y + z = 2

We know that,

AX = B

i.e.

∴ X = A^-1 B

So, firstly, we have to find the A^-1 and

Firstly, we find |A|

Expanding |A| along C₁, we get

= 3(2 + 3) – 1(2 – 2) + 2(6 + 4)

= 3(5) + 2(10)

= 15 + 20

= 35

Now, we have to find adj A and for that we have to find co-factors:

Now, X = A^-1B

∴ x = 1, y = 1 and z = 1