Question

If in the determinant$\Delta = \left| \begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix} \right|$, $A_{1},B_{1},C_{1}$ etc. be the co-factors of $a_{1},b_{1},c_{1}$etc., then which of the following relations is incorrect.

• A. $a_{1}A_{1} + b_{1}B_{1} + c_{1}C_{1} = \Delta$
• B. $a_{2}A_{2} + b_{2}B_{2} + c_{2}C_{2} = \Delta$
• C. $a_{3}A_{3} + b_{3}B_{3} + c_{3}C_{3} = \Delta$
• D. $a_{1}A_{2} + b_{1}B_{2} + c_{1}C_{2} = \Delta$

Answer 1

Answer: (D)

$a_{1}A_{2} + b_{1}B_{2} + c_{1}C_{2} = \Delta$

Answer 2

It is a fundamental concept.