Question

How do you find the determinant of `((1, 3, 5), (1, 1, 3), (2, 8, 12))`?

Answer 1

`|(1, 3, 5), (1, 1, 3), (2, 8 , 12)| = 0`

Explanation:

Expanding using row1 we have;

`|(1, 3, 5), (1, 1, 3), (2, 8 , 12)| = (1)|(1, 3), (8 , 12)| - (3)|(1,3), (2, 12)| + (5)|(1, 1), (2,8)|`

`= (1){(1)(12)-(8)(3)} - (3){(1)(12)-(2)(3)} + (5){(1)(8)-(2)(1)}`
`= (1)(12-24) - (3)(12-6) + (5)(8-2)`
`= (1)(-12) - (3)(6) + (5)(6)`
`= -12 - 18 + 30`
`= 0`