Q. 105.0( 2 Votes )

# 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 = I_{n}A

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

I_{n} = BA

(iv) Write A^{-1} = B

Now,

We have,

A = I_{3}A

Where I_{3} 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^{-1}A

Therefore

A^{-1} = B

⇒ inverse of A

Rate this question :

Using matrices, solve the following system of equations:

2x + 3y + 3z = 5, x – 2y + z = – 4, 3x – y – 2z = 3

Mathematics - Board PapersIf find Using solve the system of equation

Mathematics - Board PapersSolve for using properties of determinants.

**OR**

Using elementary row operations find the inverse of a matrix and hence solve the following system of equations

Mathematics - Board Papers