Question

Suppose $D = \left| \begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix} \right|$ and

$D^{'} = \left| \begin{matrix} a_{1} + pb_{1} & b_{1} + qc_{1} & c_{1} + ra_{1} \\ a_{2} + pb_{2} & b_{2} + qc_{2} & c_{2} + ra_{2} \\ a_{3} + pb_{3} & b_{3} + qc_{3} & c_{3} + ra_{3} \end{matrix} \right|$, then.

• A. $D^{'} = D$
• B. $D^{'} = D(1 - pqr)$
• C. $D^{'} = D(1 + p + q + r)$
• D. $D^{'} = D(1 + pqr)$

Answer 1

Answer: (D)

$D^{'} = D(1 + pqr)$

Answer 2

$D^{'} = D + pqrD = D(1 + pqr)$.

Trick : Check by putting $B = I$ and all other zero.