Let $M$ be a $3 imes 3$ matrix satisfying $M\left[\begin{array}{l}0 \ 1 \ 0\end{array} ight]=\l

Question

Let $M$ be a $3 	imes 3$ matrix satisfying $M\left[\begin{array}{l}0 \ 1 \ 0\end{array}ight]=\left[\begin{array}{c}-1 \ 2 \ 3\end{array}ight]$, $M\left[\begin{array}{c}1 \ -1 \ 0\end{array}ight]=\left[\begin{array}{c}1 \ 1 \ -1\end{array}ight]$, and $M\left[\begin{array}{l}1 \ 1 \ 1\end{array}ight]=\left[\begin{array}{c}0 \ 0 \ 12\end{array}ight]$. Then the sum of the diagonal entries of $M$ is

Professor PC Thomas Classes · Answer

(9) : Let $M=\left[\begin{array}{lll}a & b & c \ d & e & f \ g & h & i\end{array}ight] \quad a=0$\ from the system of equations we get $e=2\}$ $i=7$ \}\ by solving simultaneous equation.\ Sum of diagonal entries $=0+2+7=9$.\