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}