# Find the determinant of the following matrices. begin{bmatrix}4 & 1 &0 -1 &7&-2 2&3&5 end{bmatrix}

Find the determinant of the following matrices.
$\left[\begin{array}{ccc}4& 1& 0\\ -1& 7& -2\\ 2& 3& 5\end{array}\right]$
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Gennenzip
Step 1
Given matrix : $\left[\begin{array}{ccc}4& 1& 0\\ -1& 7& -2\\ 2& 3& 5\end{array}\right]$ we have to find determinant of the given matrices.
Step 2
$\left[\begin{array}{ccc}4& 1& 0\\ -1& 7& -2\\ 2& 3& 5\end{array}\right]$ expand along row 1
$\left[\begin{array}{ccc}4& 1& 0\\ -1& 7& -2\\ 2& 3& 5\end{array}\right]=4\left(7\left(5\right)-3\left(-2\right)-1\left(\left(-1\right)5-\left(-2\right)2\right)+0\right)$
$=4\left(35+6\right)-1\left(-5+4\right)$
$=4\left(41\right)-1\left(-1\right)=164+1=165$ the required answer is
$\left[\begin{array}{ccc}4& 1& 0\\ -1& 7& -2\\ 2& 3& 5\end{array}\right]=165$
Jeffrey Jordon