Q. Which of the following determinant(s) vanish(es) ?

392 161 Determinants Report Error

A

$∣ ∣ 111 b c c a ab b c (b + c) c a (c + a) ab (a + b) ∣ ∣$

B

$∣ ∣ 111 ab bc c a \frac{1}{a} + \frac{1}{b} \frac{1}{b} + \frac{1}{c} \frac{1}{c} + \frac{1}{a} ∣ ∣$

C

$∣ ∣ 0 b - a c - a a - b 0 c - b a - c b - c 0 ∣ ∣$

D

$∣ ∣ lo g_{x} x yz lo g_{y} x yz lo g_{z} x yz lo g_{x} y 1 lo g_{z} y lo g_{x} z lo g_{y} z 1 ∣ ∣$

Solution:

Correct answer is (a) $∣ ∣ 111 b c c a ab b c (b + c) c a (c + a) ab (a + b) ∣ ∣$ Correct answer is (b) $∣ ∣ 111 ab bc c a \frac{1}{a} + \frac{1}{b} \frac{1}{b} + \frac{1}{c} \frac{1}{c} + \frac{1}{a} ∣ ∣$ Correct answer is (c) $∣ ∣ 0 b - a c - a a - b 0 c - b a - c b - c 0 ∣ ∣$ Correct answer is (d) $∣ ∣ lo g_{x} x yz lo g_{y} x yz lo g_{z} x yz lo g_{x} y 1 lo g_{z} y lo g_{x} z lo g_{y} z 1 ∣ ∣$