Find a basis of the linear space V of all 2x2 matrices A for which

[1; -3] is an eigenvector, and thus determine the dimension of V (; denotes a new row).

Attempt at a solution:

So A[1; -3] = (lambda)[1; -3].

[a b; c d][1; -3] = (lambda)[1; -3]. Here I'm stuck--is this even the right direction to go in?