# How do you find the determinant of ((2, 2, 5), (-3, -1, 2), (0, 4, -2))?

Feb 9, 2016

$| \left(2 , 2 , 5\right) , \left(- 3 , - 1 , 2\right) , \left(0 , 4 , - 2\right) | = - 60$

#### Explanation:

$| \left(\textcolor{red}{2} , \textcolor{b l u e}{2} , \textcolor{g r e e n}{5}\right) , \left(- 3 , - 1 , 2\right) , \left(0 , 4 , - 2\right) |$

$\textcolor{w h i t e}{\text{XXXXXX}} = \textcolor{red}{2 \times | \left(- 1 , 2\right) , \left(4 , - 2\right) |} - \textcolor{b l u e}{2 \times | \left(- 3 , 2\right) , \left(0 , - 2\right) |} + \textcolor{g r e e n}{5 \times | \left(- 3 , - 1\right) , \left(0 , 4\right) |}$

$\textcolor{w h i t e}{\text{XXXXXX}} = \textcolor{red}{2 \left(2 - 8\right)} - \textcolor{b l u e}{2 \left(6 - 0\right)} + \textcolor{g r e e n}{5 \left(- 12 - 0\right)}$

$\textcolor{w h i t e}{\text{XXXXXX}} = \left(\textcolor{red}{- 12}\right) - \left(\textcolor{b l u e}{- 12}\right) + \left(\textcolor{g r e e n}{- 60}\right)$

$\textcolor{w h i t e}{\text{XXXXXX}} = - 60$