Q. 15

Find the inverse of each of the following matrices by using elementary row transformations:


Answer :

Given:- 3 x 3 square matrix


Tip:- Algorithm to find Inverse of a square matrix of ‘n’ order by elementary row transformation


(i) Obtain the square matrix, say A


(ii) Write A = InA


(iii) Perform a sequence of elementary row operation successively on A on the LHS and pre-factor In on the RHS till we obtain the result


In = BA


(iv) Write A-1 = B


Now,


We have,


A = I3A


Where I3 is 3 x 3 elementary matrix



Applying



Applying



Applying and



Applying



Applying and



Hence , it is of the form


I = BA


So, as we know that


I = A-1A


Therefore


A-1 = B


inverse of A


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