Sum

Use elementary column operation C_{2} → C_{2} + 2C_{1} in the following matrix equation :

`[[2,1],[2,0]] = [[3,1],[2,0]] [[1,0],[-1,1]]`

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#### Solution

The given matrix equation is in the form X =AB.

In order to apply elementary column operation on X =AB, we apply it simultaneously on X and on B of the product AB on RHS.

`[[2 , 1], [2 , 0]] = [[2 , 1], [2 , 0]]`

X = AB

We apply the transformation on the first and third matrices.

Apply C_{2} → C_{2} + 2C_{1}

`[[2 , 1 + 4], [2, 0 + 4]] = [[3, 1],[2, 0]][[1, 0 + 2],[ -1, 1 - 2]]`

⇒ `[[2 , 5],[2, 4]] = [[3, 1],[2, 0]] [[1, 2],[-1 , -1]]`

Now you can clearly see that equation is satisfied.

Concept: Elementary Transformations

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