(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.
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?