Question

How do you find the determinant of `((2, 11, -3, 1), (1, 5, 7, -4), (6, 13, -5, 2), (4, 22, -6, 2))`?

Answer 1

`0`

Explanation:

`((color(blue)(2),color(blue)(11),color(blue)(-3),color(blue)(1)),(1,5,7,-4),(6,13,-5,2),(color(crimson)(4),color(crimson)(22),color(crimson)(-6),color(crimson)(2)))=2*((color(blue)(2),color(blue)(11),color(blue)(-3),color(blue)(1)),(1,5,7,-4),(6,13,-5,2),(color(crimson)(2),color(crimson)(11),color(crimson)(-3),color(crimson)(1)))`

When a determinant has two lines or 2 columns equal (or what leads to the same conclusion, when it has two lines or 2 columns proportional), this determinant is equal to zero.

Therefore, since, in the present case, row1 `=` row4 :
`Det.=0`