3x3 Matrix
Find the determinant of the shown 3 x 3 matrix:
Expand Hint
$$$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}=a\cdot\begin{vmatrix}e & f\\ h & i\end{vmatrix}-b\cdot \begin{vmatrix}d & f\\ g & i\end{vmatrix}+c\cdot \begin{vmatrix}d & e\\ g & h\end{vmatrix}$$$
Hint 2
$$$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$$$
For a third-order determinant:
$$$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}=a\cdot\begin{vmatrix}e & f\\ h & i\end{vmatrix}-b\cdot \begin{vmatrix}d & f\\ g & i\end{vmatrix}+c\cdot \begin{vmatrix}d & e\\ g & h\end{vmatrix}$$$
$$$\begin{bmatrix}a & b & c\\ d & e & f\\ g & h & i\end{bmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$$$
Thus,
$$$\begin{bmatrix}0 & 3 & 5\\ 1 & 2 & 4\\ 10 & 6 & -1\end{bmatrix}=0[(2)(-1)-(4)(6)]-3[(1)(-1)-(4)(10)]+5[(1)(6)-(2)(10)]$$$
$$$=0-3[(-1)-40]+5[6-20]$$$
$$$=0-3[-41]+5[-14]=123-70=53$$$
53
Time Analysis
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