Let T:V->W Be A Linear Transformation

Where V and W are vector spaces over a Field F

let a={v_{1},v_{2},...,v_{n}} be a basis for V and b={w_{1},w_{2},....,w_{m}} be a basis for W

a) Prove that T is surjective if and only if the columns of [T]_{ba}span F^{n }

b) Prove that T is injective if and only if the columns of [T]_{ba}are linearly independent in F^{n}