Question

Using cofactors of the elements of second column,evaluate the following
| 2 3 -2 |
| 1 2 3 |
| -2 1 -3 |

Answer 1

Answer:

$\bf{\left|\begin{array}{ccc}2&3&-2\\1&2&3\\-2&1&-3\end{array}\right|=-37}$

Step-by-step explanation:

$\left|\begin{array}{ccc}2&3&-2\\1&2&3\\-2&1&-3\end{array}\right|$

Expanding along Column 2

$=3(-\left|\begin{array}{cc}1&3\\-2&-3\end{array}\right|)+2\left|\begin{array}{cc}2&-2\\-2&-3\end{array}\right|+1(-\left|\begin{array}{cc}2&-2\\1&3\end{array}\right|)$

$=-3(-3+6)+2(-6-4)-1(6+2)$

$=-9-20-8$

$=-37$

$\implies\:\bf{\left|\begin{array}{ccc}2&3&-2\\1&2&3\\-2&1&-3\end{array}\right|=-37}$