Question

The determinant $\left| \begin{matrix} a & b & a - b \\ b & c & b - c \\ 2 & 1 & 0 \end{matrix} \right|$ is equal to zero if $a,b,c$are in.

• A. G. P.
• B. A. P.
• C. H. P.
• D. None of these

Answer 1

Answer: (A)

G. P.

Answer 2

On expanding,

$- a(b - c) + 2b(b - c) + (a - b)(b - 2c) = 0$

⇒ $- ab + ac + 2b^{2} - 2bc + ab - 2ac - b^{2} + 2bc = 0$

⇒ $b^{2} - ac = 0$ ⇒ $b^{2} = ac$.