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Question
Prove that: `|("a"^2 + 2"a", 2"a" + 1, 1),(2"a" + 1, "a" + 2, 1),(3, 3, 1)| = ("a" - 1)^3`
Solution
`|("a"^2 + 2"a", 2"a" + 1, 1),(2"a" + 1, "a" + 2, 1),(3, 3, 1)|`
[Applying R1 → R1 – R2 and R2 → R2 – R3]
= `|("a"^2 - 1, "a" - 1, 0),(2"a" - 2, "a" - 1, 0),(3, 3, 1)|`
[Taking (a – 1) common from R1 and R2]
`("a" - 1)^2 |("a" + 1, 1, 0),(2, 1, 0),(3, 3, 1)|`
[Expanding along R3]
= `("a" - 1)^2 [1 * ("a" + 1) - 2]`
= (a – 1)3
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