GATE Civil Engineering (CE) 2020 Shift 2 Solved Paper

$\left|\mathit{P}\right|=-\left(-2\right)|\begin{array}{ccc}1& 3& 0\\ 0& 6& 1\\ 0& 1& 6\end{array}|$
$=2|\begin{array}{ccc}1& 3& 0\\ 0& 6& 1\\ 0& 1& 6\end{array}|$
$\left|\mathit{P}\right|=70$
As, the determinant of the given matrix is non-zero
Hence, the matrix is singular.
The product of eigen values $=|\mathit{A}|$
${\mathit{\lambda }}_1,{\mathit{\lambda }}_2,{\mathit{\lambda }}_3,{\mathit{\lambda }}_4=70$
sum of eigen values $=$ trace of matrix $\mathit{P}$
trace of matrix $\mathit{P}=0+3+6+6$
=15
${\mathit{\lambda }}_1+{\mathit{\lambda }}_2+{\mathit{\lambda }}_3+{\mathit{\lambda }}_4=50$
Checking the above options, only (B) option is correct.
${\mathit{\lambda }}_1,{\mathit{\lambda }}_2,{\mathit{\lambda }}_3,{\mathit{\lambda }}_4,=1,2,5,7$