Question

Let D = $\left| \begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix} \right|$& 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(1 + p + q + r)
• B. D' = D(1 + pqr)
• C. D' = D
• D. None

Answer 1

Answer: (B)

D' = D(1 + pqr)

Answer 2

D' = $\left| \begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix} \right|$ + $\left| \begin{matrix} pb_{1} & qc_{1} & ra_{1} \\ pb_{2} & qc_{2} & ra_{2} \\ pb_{3} & qc_{3} & ra_{3} \end{matrix} \right|$ = (1 + pqr) D