Question

Evaluate the determinant of the matrix..

Answer 1

you'd get the cofactors, multiply by the minors determinant
and use the "checkerboard" signs for hte cofactor

does it ring a bell?

Answer 2

isnt there a formula for 3x3's?

Answer 3

nope, there's one for a 2x2
for a 3x3 and up, you have to use the minors and cofactors and checkerboard signs

\(\large {
\begin{bmatrix}
-4&5&6\\ 0&4&4\\-2&-5&4
\end{bmatrix}\qquad
\begin{array}{llll}
checkboard\ signs\\

\begin{bmatrix}
+&-&+\\-&+&-\\+&-&+
\end{bmatrix}
\end{array}
\\ \quad \\

\begin{array}{llll}
\textit{sum of their determinants, using the }{\color{blue}{ cofactors}}\\
\begin{bmatrix}
{\color{blue}{ -4}}&&\\ &4&4\\&-5&4
\end{bmatrix}+\begin{bmatrix}
&5&6\\ {\color{blue}{ 0}}&&\\&-5&4
\end{bmatrix}+
\begin{bmatrix}
&5&6\\ &4&4\\{\color{blue}{ -2}}&&
\end{bmatrix}
\end{array}
}\)

Answer 4

this is a really pellettttttty drawing but isnt like this? and then you multiply the groups of 3 together,,,