Write the Value of ∣ ∣ ∣ ∣ a − B B − C C − a B − C C − a A − B C − a A − B B − C ∣ ∣ ∣ ∣ - Mathematics

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Sum

Write the value of `|(a-b, b- c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|`

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Solution

Let Δ = `|(a-b, b- c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|`   

By R1 → R1 + R2 + R3

⇒ Δ = `|(0, 0, 0),(b-c, c-a, a-b),(c-a, a-b, b-c)|` = 0  ...(as all elements of R1 are zero).

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2015-2016 (March) All India Set 1 E

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