in properties of determinants how do we apply c1-c1+c2+c3 or ri-r1+r2+r3 in any row or column plz xplain wid an example

First of all make it clear in your mind that what elementary transformations you can apply to find the inverse of matrix.

The elementary transformations that can be applied to a matrix are:

1. Interchange of any two rows or columns of a matrix

It is denoted as R_{i} ↔ R*j *or C_{i} ↔ C_{j}

2. Elements of any row or column multiplied by a non-zero number

It can be denoted as R*i* ↔ *k*R*i *of C*i* ↔ *k*C*i*,where *k *is a non-zero constant.

3. Addition to the elements of any row or column; the corresponding elements of any other row

or column multiplied by any non-zero number.

It is denoted as R_{i} → R_{i} + *k*R_{j} or C_{i} → C_{i} + *k*C_{j}.

Using these operations we can find the inverse of a given matrix. The steps of algorithm to find the inverse of given matrix are:

**Step 1. **Obtain the square matrix, say A

**Step 2.** Write A = I_{n }A

**Step 3. **Perform the sequence of elementary operations on A on the LHS and the pre-factor I_{n }on the RHS till we obtain the result I_{n} = BA

**Step 4. **Write A^{-1} = B

Here is an example to find the inverse of the given matrix, using the elementary row operations:

Find the inverse of the matrix.

Solution:

Let

Now, *A* = *IA*

∴

After getting this concept,you are suggested to go through the study material again. This

concept is explained nicely with the help of video in our study material.That will help you a lot.

Still if you face any problem, then do get back to us.

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