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Question
If A = `[(2,1,3),(1,0,1),(1,1,1)]`, then reduce it to I3 by using row transformations.
Solution
|A| = `|(2,1,3),(1,0,1),(1,1,1)|`
= 2(0 - 1)- 1(1 - 1) + 3(1 - 0)
= - 2 - 0 + 3
= 1 ≠ 0
∴ A is a non-singular matrix.
Hence, the required transformation is possible.
Now, A = `[(2,1,3),(1,0,1),(1,1,1)]`
By R1 - R2, we get,
A ∼ `[(1,1,2),(1,0,1),(1,1,1)]`
By R2 - R1 and R3 - R1, we get,
A ∼ `[(1,1,2),(0,-1,-1),(0,0,-1)]`
By (- 1)R2 and (- 1)R3, we get,
A ∼ `[(1,1,2),(0,1,1),(0,0,1)]`
By R1 - R2, we get,
A ∼ `[(1,0,1),(0,1,1),(0,0,1)]`
By R1 - R3, and R2 - R3, we get,
A ∼ `[(1,0,0),(0,1,0),(0,0,1)]` = I3
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