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Question
Use elementary column operation C2 → C2 + 2C1 in the following matrix equation :
`[[2,1],[2,0]] = [[3,1],[2,0]] [[1,0],[-1,1]]`
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 C2 → C2 + 2C1
`[[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.
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