3x3 Determinant
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,
$$$\begin{bmatrix}1 & 2 & 0\\ 1 & 1 & 1\\ 2 & 2 & 0\end{bmatrix}=1[(1)(0)-(1)(2)]-2[(1)(0)-(1)(2)]+0[(1)(2)-(1)(2)]$$$
$$$=1[0-2]-2[0-2]+0$$$
$$$=1(-2)-2(-2)+0=-2+4=2$$$
2
Time Analysis
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