MCQ
$\left| {\,\begin{array}{*{20}{c}}{19}&{17}&{15}\\9&8&7\\1&1&1\end{array}\,} \right| = $
- ✓$0$
- B$187$
- C$354$
- D$54$
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$E_1=\{A \in S: \operatorname{det} A=0\} \text { and }$ $E_2=\{A \in S: \text { sum of entries of } A \text { is } 7\}.$ If a matrix is chosen at random from $S$, then the conditional probability $P\left(E_1 \mid E_2\right)$ equals. . . . . . . .
$7 x+11 y+\alpha z=13$
$5 x+4 y+7 z=\beta$
$175 x+194 y+57 z=361$
has infinitely many solutions, then $\alpha+\beta+2$ is equal to