Determinants (do you notice any thing wrong??)
Hi guys,
hoping somebody can check through my calculations for the determinant of $\displaystyle A$ a 4 x 4 matrix.
$\displaystyle A = \begin{vmatrix}
\-1 && 3 && 0 && 5 \\
-2 && 0 && 4 && 0\\
1 && 2 && -1 && 3\\
1 && -2 && 1 && -1\\
\end{vmatrix} = 1 \begin{vmatrix}
\ 0 && 4 && 0 \\
2 && -1 && 3\\
-2 && 1 && -1\\
\end{vmatrix} - 3 \begin{vmatrix}
\ -2 && 4 && 0 \\
1 && -1 && 3\\
1 && 1 && -1\\
\end{vmatrix}
$
$\displaystyle
+ 0 \begin{vmatrix}
\ -2 && 0 && 0 \\
1 && 2 && 3\\
1 && -2 && -1\\
\end{vmatrix} - 5 \begin{vmatrix}
\ -2 && 0 && 4 \\
1 && 2 && -1\\
1 && -2 && 1\\
\end{vmatrix}
$
$\displaystyle
= 1det(4)\begin{vmatrix}
\ 2 && 3 \\
-2 && -1\\
\end{vmatrix}
$
$\displaystyle
- 3 det(-2) \begin{vmatrix}
\ -1 && 3 \\
1 && -1\\
\end{vmatrix} - det(4) \begin{vmatrix}
\ 1 && 3 \\
1 && -1\\
\end{vmatrix}
$
$\displaystyle
- 5det(-2) \begin{vmatrix}
\ 2 && -1 \\
-2 && 1\\
\end{vmatrix} + det(4) \begin{vmatrix}
\ 1 && 2 \\
1 && -2\\
\end{vmatrix}
$
$\displaystyle = 1 (4(-2+6) - 3 (-2(1-3) - 4(-1-3))-5(-2(2-2)+4(-2-2))$
$\displaystyle = 1 (4(4) - 3 (-2(-2) - 4(-4))-5(-2(0) + 4(-4))$
$\displaystyle = 1 (16) - 3 (4 + 16) +5(-16) $
If anyone noticed any wrong be greatly appreciate if they could correct it saying so.
Thanks a bunch!