Thread: Determinant and Linear Dependence

Hi,

a 3x3 matrix with the determimant zero means that the three column vecorts are linear dependent.

two questions about that:

1.) Is this also correct for a 4x4 matrix?

2.) Is this argument with the determinant if we are talking about linear dependence for all matrices valid, or only for quadratic matrices?

Thanks
Greetings

Hi!

(1) This is valid for any nxn matrix: det(A) nonzerto iff columns, rows respectively are linearly independent.

(2) The determinant is only defined for square matrices.