question_answer

Maximum value of the determinant of order third formed by the elements 0 & 1 only is

A) 3

B) 2

C) 1

D) none of these

Correct Answer: B

Solution :

Let \[D=\left| \begin{matrix}    {{a}_{11}} & {{a}_{12}} & {{a}_{13}}  \\    {{a}_{21}} & {{a}_{22}} & {{a}_{23}}  \\    {{a}_{31}} & {{a}_{32}} & {{a}_{33}}  \\ \end{matrix} \right|\]

for maximum value we have to assign maximum value to the +ve term & minimum value to \[ve\]term which is possible if three elements will become zero of different row & different column.

\[\therefore \]    i.e. \[{{a}_{13}}={{a}_{21}}={{a}_{32}}=0\]& \[{{a}_{11}}={{a}_{32}}={{a}_{33}}={{a}_{12}}\]

\[\therefore \]    \[{{D}_{\max }}=2-0=2\]