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