linearly DEpendent.

we always know that (0,0) is a solution. so if we have any OTHER solution, A cannot be invertible.

well, if a = b = 0, then if c = 0, we have the non-zero solution (1,0), and if d = 0, we have the non-zero solution (0,1).

otherwise, we have the non-zero solution (1,-c/d).

so suppose a is non-zero. then we have the non-zero solution (-b/a,1).

why does this show A is non-invertible?

if we have Ax=0, withx≠0then what do we choose for the value A^{-1}(0)?