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Question
Apply the given elementary transformation of the following matrix.
Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row transformations.
Solution
Let A `[(1,-1),(2,3)]`
∴ |A| = `[(1,-1),(2,3)]`
= 3 + 2 = 5 ≠ 0
∴ A is a non-singular matrix.
Hence, row transformations are possible.
Now A = `[(1,-1),(2,3)]`
Applying R2→ R2 - 2R1, we get
A ~ `[(1,-1),(0,5)]`
Applying R2 → `(1/5)`R2, we get
A ~ `[(1,-1),(0,1)]`
Applying R1 → R1 + R2, we get
A ~ `[(1, 0), (0,1)]`, which is an identity matrix.
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