Question

Find the cofactors of elements $a_{12},a_{22},a_{32}$, respectively of the matrix $\left[\begin{array}{ccc}1& sin\theta & 1\\ -sin\theta & 1& sin\theta \\ -1& -sin\theta & 1\end{array}\right]$

• A. $0,2,-2\sin \theta$
• B. $2,0,2\sin \theta$
• C. $2,0,-2\sin \theta$
• D. $-2\sin \theta ,2,0$

Answer 1

Answer: (A)

$M_{12}=\left|\begin{array}{cc}-sin\theta & sin\theta \\ -1& 1\end{array}\right|=-sin\theta +sin\theta =0$
$\Rightarrow c_{12}=-M_{12}=0$
$M_{22}=\left|\begin{array}{cc}1& 1\\ -1& 1\end{array}\right|=1+1=2$
$\Rightarrow C_{22}=M_{22}=2$
$M_{32}=\left|\begin{array}{cc}1& 1\\ -sin\theta & sin\theta \end{array}\right|=sin\theta +sin\theta =2sin\theta$
$c_{32}=-M_{32}=-2sin\theta$