# Find the determinate A=begin{bmatrix}4 & 1 3 & 2 end{bmatrix} B=begin{bmatrix}2 & 0&1 0 & 1&00&2&1 end{bmatrix} C=begin{bmatrix}3 & -2&0 -2 & 3&00&0&0 end{bmatrix}

Find the determinate
$A=\left[\begin{array}{cc}4& 1\\ 3& 2\end{array}\right]$
$B=\left[\begin{array}{ccc}2& 0& 1\\ 0& 1& 0\\ 0& 2& 1\end{array}\right]$
$C=\left[\begin{array}{ccc}3& -2& 0\\ -2& 3& 0\\ 0& 0& 0\end{array}\right]$
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Step 1
For the $2×2$ matrix we can find determinants by multiplying the diagonal numbers and find the difference between their products. For other square matrices, we have to expand along row or column as seen in the below steps to find the determinant.
Step 2
(1)$A=\left[\begin{array}{cc}4& 1\\ 3& 2\end{array}\right]$
$|A|=4×2-3×1=8-3=5$
Determinant of A is 5
Step 3
(2) $B=\left[\begin{array}{ccc}2& 0& 1\\ 0& 1& 0\\ 0& 2& 1\end{array}\right]$
$|B|=2\left(1-2×0\right)-0\left(0-0\right)+1\left(0-0\right)$
=2
Determinant of B is 2
Step 4
(3) $C=\left[\begin{array}{ccc}3& -2& 0\\ -2& 3& 0\\ 0& 0& 0\end{array}\right]$

$|C|=3\left(3×0-0×0\right)+2\left(-2×0-0×0\right)+0\left(2×0-3×0\right)$
$=3×0+2×0+0=0$
Determinant of C is 0

Jeffrey Jordon