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

Jul 10, 2016

You can not manipulate this matrix into the form

$\left[\begin{matrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right]$

So it does not have a determinate

#### Explanation:

$\left[\begin{matrix}1 & - 1 & 2 \text{ | " 1 & 0 & 0 \\ 0 & 3 & 0" | "0 & 1 & 0 \\ 1 & 2 & 2" | } 0 & 0 & 1\end{matrix}\right]$
$R o w \left(2\right) \div 3$
$\text{ } \downarrow$
$\textcolor{w h i t e}{.}$

$\left[\begin{matrix}1 & - 1 & 2 \text{ | " 1 & 0 & 0 \\ 0 & 1 & 0" | "0 & 1/3 & 0 \\ 1 & 2 & 2" | } 0 & 0 & 1\end{matrix}\right]$
$R o w \left(3\right) - R o w \left(1\right)$
$\text{ } \downarrow$
$\textcolor{w h i t e}{.}$

$\left[\begin{matrix}1 & - 1 & 2 \text{ | " 1 & 0 & 0 \\ 0 & 1 & 0" | "0 & 1/3 & 0 \\ 0 & 3 & 0" | } - 1 & 0 & 1\end{matrix}\right]$
$R o w \left(3\right) - R o w \left(1\right)$
$\text{ } \downarrow$
$\textcolor{w h i t e}{.}$

You can not manipulate this matrix into the form

$\left[\begin{matrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right]$

So it does not have a determinate