Q. 173.7( 29 Votes )

Using elementary

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| = [(2) {1×3 – 1 × (0)} – (0) {3 × 5 – 0 × 0} + (-1) {5 × 1 – 1 × 0}]


= [2{3} - 0 {15} - 1 {5}]


= [6-0-5]


= 1


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- R1 R1



Apply row operation- R2 R2 -5R1



Apply row operation- R3 R3 – R2



Apply row operation- R1 R1 + R3



Apply row operation- R2 R2 –5R3



Apply row operation- R3 2R3



The matrix so obtained is of the form –


[I : A-1]


Hence inverse of the given matrix-



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