# How do you find the determinant of ((1, 1, 1,), (1, 2, 3), (3, 2, 1))?

Feb 9, 2016

$| \left(1 , 1 , 1\right) , \left(1 , 2 , 3\right) , \left(3 , 2 , 1\right) | = 0$

#### Explanation:

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

color(white)("XXXXXX")=color(red)(1xx|(2,3),(2,1)|)-color(blue)(1xx|(1,3),(3,1)|+color(green)(1xx|(1,2),(3,2)|

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

$\textcolor{w h i t e}{\text{XXXXXX}} = \textcolor{red}{- 4} - \left(\textcolor{b l u e}{- 8}\right) + \textcolor{g r e e n}{- 4}$

$\textcolor{w h i t e}{\text{XXXXXX}} = 0$