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  4. If M11=-40, M12=-10 and M13=35 of the determinant Δ=|1 3 -2 4 -5 6 3 5 2|, then the value of Δ is

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Q. If $M_{11}=-40, M_{12}=-10$ and $M_{13}=35$ of the determinant $\Delta=\begin{vmatrix}1 & 3 & -2 \\ 4 & -5 & 6 \\ 3 & 5 & 2\end{vmatrix}$, then the value of $\Delta$ is

Determinants

Solution:

Given that, $\Delta=\begin{vmatrix}1 & 3 & -2 \\ 4 & -5 & 6 \\ 3 & 5 & 2\end{vmatrix}$
Also, $ M_{11}=-40, M_{12}=-10$ and $M_{13}=35$
$\therefore A_{11}=(-1)^{1+1} M_{11}=-40$
$A_{12}=(-1)^{1+2} M_{12}$
$=10$
and $ A_{13}=(-1)^{1+3} M_{13}=35$
$\therefore \Delta=a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}$
$=1 \times(-40)+3(10)+(-2)(35)$
$=-40+30-70$
$=-80$