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Question
Solve the following :
If A = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`, the reduce it to unit matrix by using row transformations.
Solution
AB = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`
∴ |A| = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`
= 1(1 – 0) –0(2 –0) + 0(6 – 3)
= 1 – 0 + 0
= 1 ≠ 0
∴ A is non-singular matrix.
Hence, row transformations are possible.
Now, A = `[(1, 0, 0),(2, 1, 0),(3, 3, 1)]`
Applying R2 → R2 – 2R1 and R3 → R3 – 3R1, we get
A = `[(1, 0, 0),(0, 1, 0),(0, 3, 1)]`
Applying R3 → R3 – 3R2, we get
A = `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`.
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