# Math Help - Help with a practice linear algebra proof?

1. ## Help with a practice linear algebra proof?

Came across this in a practice problem book, and I'm stuck on it. Any help would be appreciated! =)

Let V and W be finite-dimensional vector spaces and T:V ---> W be an isomorphism. Let Vo be a subspace of V.
a) Prove that T(Vo) is a subspace of W.
b) Prove that dim(Vo) = dim(T(Vo)).

2. Originally Posted by paupsers
Came across this in a practice problem book, and I'm stuck on it. Any help would be appreciated! =)

Let V and W be finite-dimensional vector spaces and T:V ---> W be an isomorphism. Let Vo be a subspace of V.
a) Prove that T(Vo) is a subspace of W.
b) Prove that dim(Vo) = dim(T(Vo)).
a) just follow the definition of a subspace.

b) choose a basis $\{v_1, \cdots , v_m \}$ for $V_0$ and show that $\{T(v_1), \cdots , T(v_m) \}$ is a basis for $T(V_0).$