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+1 vote
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in Mathematics by (64.8k points)

Prove that |(a, a + b, a + b + c), (2a, 3a + 2b, 4a + 3b + 2c), (3a, 6a + 3b, 10a + 6b + 3c)| = a3

1 Answer

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Applying operations R2 → R2 – 2R1 and R3 → R3 – 3R1 to the given determinant Δ, we have

Now applying R3 → R3 – 3R2 , we get

Expanding along C1, we obtain

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