Question

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

• A. $-80$
• B. 60
• C. 70
• D. 100

Answer 1

Answer: (A)

Given that, $\Delta =\left|\begin{array}{ccc}1& 3& -2\\ 4& -5& 6\\ 3& 5& 2\end{array}\right|$
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 $A_{13}=(-1{)}^{1+3}{M}_{13}=35$
$\therefore \Delta =a_{11}{A}_{11}+a_{12}{A}_{12}+a_{13}{A}_{13}$
$=1\times (-40)+3(10)+(-2)(35)$
$=-40+30-70$
$=-80$