Q. 51 A5.0( 1 Vote )

If possible, using elementary row transformations, find the inverse of the following matrices


Answer :

Let A =


To apply elementary row transformations we write:


A = IA where I is the identity matrix


We proceed with operations in such a way that LHS becomes I and the transformations in I give us a new matrix such that


I = XA


And this X is called inverse of A = A-1


Note: Never apply row and column transformations simultaneously over a matrix.


So we have:



Applying R2 R2 + R1


=


Applying R3 R3 - R2


=


Applying R1 R1 + R2


=


Applying R2 R2 - 3R1


=


Applying R3 (-1)R3


=


Applying R1 R1 + 10R3 and R2 R2 + 17R3


=


Applying R1 (-1)R1 and R2 (-1)R2


=


As we got Identity matrix in LHS.


A-1 =


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