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Question

The value of the determinant
Δ=∣ ∣log xlog ylog zlog 2xlog 2ylog 2zlog 3xlog 3ylog 3z∣ ∣ is



Correct Answer
A

0

Your Answer
B

log (xyz)

Your Answer
C

log (6 xyz)

Your Answer
D

6 log (xyz)


Solution

The correct option is A

0


Δ=∣ ∣log xlog ylog zlog 2xlog 2ylog 2zlog 3xlog 3ylog 3z∣ ∣

Δ=∣ ∣log xlog ylog zlog 2+log xlog 2+log ylog 2+log zlog 3+log xlog 3+log ylog 3+log z∣ ∣
(Using log (ab) =log a + log b )
Δ=∣ ∣log xlog ylog zlog 2log 2log 2log 3log 3log 3∣ ∣
(R3R3R1,R2R2R1)
=(log 2)(log 3)∣ ∣log xlog ylog z111111∣ ∣=0

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