Linear Algebra Boldrini : Theorem 5.4.5

Question

Let $T: V → W$ a linear transformation and $α$ and $β$ basis of $V$ and $W$ respectively. I want to show that $dim Im T =$ rank of matrix transformation $T$ on this basis and that $dim ker T =$ nullity of matrix transformation $T$ on this basis. I tried using $dim V = dim Im T + dim ker T$ but I could not finish what I need.