Q23 of 45 Page 1

Using matrices, solve the following system of equations:

4x + 3y + 3z = 60, x + 2y + 3z = 45 and 6x + 2y + 3z =70

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


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