# How do you find the determinant of |(25, 36, 15), (31,-12,-2), (17,15,9)|?

May 19, 2017

The answer is $= - 3183$

#### Explanation:

The determination of the determinant is as follows .

$| \left(25 , 36 , 15\right) , \left(31 , - 12 , - 2\right) , \left(17 , 15 , 9\right) |$

$= 25 | \left(- 12 , - 2\right) , \left(15 , 9\right) | - 36 | \left(31 , - 2\right) , \left(17 , 9\right) | + 15 | \left(31 , - 12\right) , \left(17 , 15\right) |$

$= 25 \left(- 12 \cdot 9 + 2 \cdot 15\right) - 36 \left(31 \cdot 9 + 17 \cdot 2\right) + 15 \left(31 \cdot 15 + 17 \cdot 12\right)$

$= 25 \cdot - 78 - 36 \cdot 313 + 15 \cdot 669$

$= - 3183$