Q. 104.4( 16 Votes )

Using elementary transformations, find the inverse of each of the matrices.


Answer :

First of all we need to check whether the matrix is invertible or not. For that-

For the inverse of a matrix A to exist,


Determinant of A ≠ 0


Here A = (3)(2) – (-1)(-4) = 2


So the matrix is invertible.


Now to find the inverse of the matrix,


We know AA-1 = I


Let’s make augmented matrix-


[ A : I ]



Apply row operation- R2 R2 + R1



Apply row operation- R1 R1/3



Apply row operation- R1 R1 + R2



Apply row operation- R2 R2



The matrix so obtained is of the form –


[ I : A-1 ]


Hence inverse of the given matrix-



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