If a- b- c are in A-P- then the determinantx-2 x-3 x-2 a x-3 x-4 x-2 b x-4 x-5 x-2 ca 0b 1c xd 2 x

(a) 0 x #160;+ #160;2 #160; #160;x #160;+ #160;3 #160; #160; #160; #160;x #160;+ #160;2ax #160;+ #160;3 #160; #160; #160;x ...

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Evaluation of a Determinant

If a, b, c ar...

Question

If a, b, c are in A.P., then the determinant

$|\begin{matrix} x + 2 & x + 3 & x + 2 a \\ x + 3 & x + 4 & x + 2 b \\ x + 4 & x + 5 & x + 2 c \end{matrix}|$

(a) 0
(b) 1
(c) x
(d) 2x

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Solution

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a, b, c

∣ ∣ ∣ ∣ \begin{matrix} x + 2 & x + 3 & x + 2 a x + 3 & x + 4 & x + 2 b x + 4 & x + 5 & x + 2 c \end{matrix} ∣ ∣ ∣ ∣

a, b

c

A P

∣ ∣ ∣ ∣ \begin{matrix} x + 2 & x + 3 & x + 2 a x + 3 & x + 4 & x + 2 b x + 4 & x + 5 & x + 2 c \end{matrix} ∣ ∣ ∣ ∣

a, b, c

∣ ∣ ∣ ∣ \begin{matrix} x + 2 & x + 3 & x + 2 a x + 3 & x + 4 & x + 2 b x + 4 & x + 5 & x + 2 c \end{matrix} ∣ ∣ ∣ ∣ = 0

∣ ∣ ∣ ∣ \begin{matrix} x + 1 & x + 2 & x + a x + 2 & x + 3 & x + b x + 3 & x + 4 & x + c \end{matrix} ∣ ∣ ∣ ∣

Choose the correct answer.

If a, b, c, are in A.P., then the determinant

A. 0 B. 1 C. x D. 2x

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