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Question: If \(\Delta_{1} = \left| \begin{matrix} 1 & 0 \\ a & b \end{matrix} \right|\) and \(\Delta_{2} = \le...

If Δ1=∣10ab∣\Delta_{1} = \left| \begin{matrix} 1 & 0 \\ a & b \end{matrix} \right| and Δ2=∣10cd∣\Delta_{2} = \left| \begin{matrix} 1 & 0 \\ c & d \end{matrix} \right|, then Δ2Δ1\Delta_{2}\Delta_{1}is equal to.

A

ac

B

bd

C

(b−a)(d−c)(b - a)(d - c)

D

None of these

Answer

bd

Explanation

Solution

Δ2Δ1=∣10cd∣∣10ab∣=∣10c+adbd∣=bd\Delta_{2}\Delta_{1} = \left| \begin{matrix} 1 & 0 \\ c & d \end{matrix} \right|\left| \begin{matrix} 1 & 0 \\ a & b \end{matrix} \right| = \left| \begin{matrix} 1 & 0 \\ c + ad & bd \end{matrix} \right| = bd.