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Question: \[\left| \begin{matrix} 1/a & 1 & bc \\ 1/b & 1 & ca \\ 1/c & 1 & ab \end{matrix} \right| =\]...

1/a & 1 & bc \\ 1/b & 1 & ca \\ 1/c & 1 & ab \end{matrix} \right| =$$
A

0

B

abc

C

1/abc

D

None of these

Answer

0

Explanation

Solution

Δ=1a[ab−ca]+1[ca.1c−1b.ab]+bc[1b−1c]\Delta = \frac{1}{a}\lbrack ab - ca\rbrack + 1\left\lbrack ca.\frac{1}{c} - \frac{1}{b}.ab \right\rbrack + bc\left\lbrack \frac{1}{b} - \frac{1}{c} \right\rbrack

⇒Δ=(b−c)+1(a−a)+(c−b)\Delta = (b - c) + 1(a - a) + (c - b) ⇒ Δ=0\Delta = 0.