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If A = (100210331), then reduce it to I3 by using column transformations. - Mathematics and Statistics

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Sum

If A = `((1,0,0),(2,1,0),(3,3,1))`, then reduce it to I3 by using column transformations.

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Solution

|A| = `|(1,0,0),(2,1,0),(3,3,1)|`

= 1(1 - 0) - 0 + 0 = 1 ≠ 0

∴ A is a non-singular matrix.

Hence, the required transformation is possible.

Now, A = `[(1,0,0),(2,1,0),(3,3,1)]`

By C1 - 2C2, we get, A ∼ `[(1,0,0),(0,1,0),(-3,3,1)]`

By C1 + 3C3 and C2 - 3C3, we get,

A ∼ `[(1,0,0),(0,1,0),(0,0,1)] = "I"_3`.

Concept: Elementry Transformations
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