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.

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

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