Find the values of the determinants [(1,-4,5)(1,1,-2)(1,3,1)]

Question

Find the values of the determinants. 

\(\begin{vmatrix}3&-4&5\\1&1&-2\\2&3&1\end{vmatrix}\)

[(1,-4,5)(1,1,-2)(1,3,1)]

Answer 1

\(\begin{vmatrix}3&-4&5\\1&1&-2\\2&3&1\end{vmatrix}\)

=\(3\begin{vmatrix}1&-2\\3&1\end{vmatrix}-(-4)\begin{vmatrix}1&-2\\2&1\end{vmatrix}+5\begin{vmatrix}1&1\\2&3\end{vmatrix}\)

= 3(1 + 6)+ 4(1 + 4)+ 5(3 – 2) 

= 3(7) + 4(5) + 5(1) 

= 21 + 20 + 5 

= 46