Question

Linear Algebra:

Suppose C is a 3 x 3 matrix such that det(C) = 2. Then det(C + C) is equal to?

Answer 1

det(c+c)=det(2c)=2^3det(c)=16

Answer 2

Thanks, can you explain where you got the exponant 3?

Answer 3

You get one two for every row. So if the first row is 2 4 6 you can get one two out of the determinant to get 1 2 3, but the other rows stay the same, so you have to do it three times.

Answer 4

Ok, so its scalar 2 times every row and since its a 3 x 3 matrix, this means that the exponant is 3?

If it was a 4 x 4 matrix, the exponant is 4? Did I understand it correctly?

Answer 5

that's right.