Question

Find the value of the determinant:

$\left|\begin{array}{ccc}15& 11& 7\\ 11& 17& 14\\ 10& 16& 13\end{array}\right|$

Answer 1

$\left|\begin{array}{ccc}15& 11& 7\\ 11& 17& 14\\ 10& 16& 13\end{array}\right|$

$=15\left(17\right(13)-16(14\left)\right)-11\left(11\right(13)-14(10\left)\right)+7\left(11\right(16)-10(17\left)\right)$

$=15(221-224)-11(143-140)+7(176-170)$

$=-45-33+42$

$=-36$