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Matrices and Determinants question

2011 · Shift 2 · Q39

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JEE Advanced
Mathematics
Matrices and Determinants
2011 · Shift 2 · Q39

Matrices and Determinants question

2011 · Shift 2 · Q39

JEE AdvancedMathematicsMatrices and DeterminantsNumerical+3 / −1

Let M be a 3

\times

3 matrix satisfying

M\left[ {\begin{matrix} 0 \\ 1 \\ 0 \\ \end{matrix} } \right] = \left[ {\begin{matrix} { - 1} \\ 2 \\ 3 \\ \end{matrix} } \right]

,

M\left[ {\begin{matrix} 1 \\ { - 1} \\ 0 \\ \end{matrix} } \right] = \left[ {\begin{matrix} 1 \\ 1 \\ { - 1} \\ \end{matrix} } \right]

and

M\left[ {\begin{matrix} 1 \\ 1 \\ 1 \\ \end{matrix} } \right] = \left[ {\begin{matrix} 0 \\ 0 \\ {12} \\ \end{matrix} } \right]

. Then the sum of the diagonal entries of M is

\underline{\hspace{2cm}}

.

Numerical answer

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