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Question
Apply the given elementary transformation on each of the following matrices `[(3, 1, -1),(1, 3, 1),(-1, 1, 3)]`, 3R2 and C2 ↔ C2 – 4C1.
Solution
Let A = `[(3, 1, -1),(1, 3, 1),(-1, 1, 3)]`
Applying R2 ↔ 3R2 , we get
`"A" ∼ [(3, 1, -1),(3, 9, 3),(-1, 1, 3)]`
Applying C2 → C2 – 4C1 on A, we get
`"A" ∼ [(3, 1 - 4(3), -1),(1, 3 - 4(1), 1),(-1, 1 - 4(-1), 3)]`
∴ `"A" ∼ [(3, 1 - 12, -1),(1, 3 - 4, 1),(-1, 1 + 4, 3)]`
∴ `"A" ∼ [(3, -11, -1),(1, -1, 1),(-1, 5, 3)]`.
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