Using matrices, solve the following system of equations:

4x + 3y + 3z = 60, x + 2y + 3z = 45 and 6x + 2y + 3z =70 (CBSE 2011)

Given, equations are –

4x + 3y + 3z = 60 …(1)

x + 2y + 3z = 45 …(2)

and 6x + 2y + 3z =70 …(3)

The above equations can be represented in matrix form as given below –

⇒ …(4)

Let,

As A^-1 =

∴ |A| =

Expanding about first row-

|A| = 4(6-6) - 3(3-18) + 3(2-12) = 45 - 30 = 15

As |A| = 15 ≠ 0, so solution is possible and unique.

Adj(A) can be determined by finding the co-factor matrix of A and taking its transpose.

Adj(A) =

∴ A^-1 =

From equation 4 we have -

By matrix multiplication we get –

⇒ ⇒

∴ x = 5 ; y = 0 and z = 40/3