Q. 51 A5.0( 1 Vote )

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

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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