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प्रश्न
Evaluate the following determinant without expanding:
`|(5, 5, 5),(a, b, c),(b + c, c + a, a + b)|`
उत्तर
Δ = `|(5, 5, 5),(a, b, c),(b + c, c + a, a + b)|`
R3 → R3 + R2
Δ = `|(5, 5, 5),(a, b, c),(a + b + c, a + b + c, a + b + c)|`
= `5 xx (a + b + c) xx |(1, 1, 1),(a, b, c),(1, 1, 1)|`
= 5(a + b + c) × 0 ...(As R1 and R3 are identical)
= 0
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