Q33 of 36 Page 1

Using the properties of determinants, prove that

OR


If , find A-1. Hence solve the system of equations x -y = 3; 2x + 3y + 4z = 17; y + 2z = 7.


Given:


To Prove:















Expanding,


=


=


=


= [Proved]


OR


Given:


To Find: A-1 and solve the system of equations x -y = 3; 2x + 3y + 4z = 17; y + 2z = 7


The given equations can be written as,


i.e.,


A Z = B


Z = A-1B


We know,



|A| = 2(-2) – 3(2) + 4(1) = -6 0. So, the system is consistent and have unique solution.


Adj(A) =


So,


A11 = -2 + 0 = -2; A12 = -(2 – 0) = -2; A13 = 1 – 0 = 1


A21 = -(6 – 4) = -2; A22 = 4 – 0 = 4; A23 = -(2 – 0) =-2


A31 = 0 – (-4) = 4; A32 = -(0 – 4) = 4; A33 = - 2 – 3 = -5


Therefore,



So,


So,



Answer: x = 2, y = -1 and z = 4


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