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Math Help - Help with a practice linear algebra proof?

  1. #1
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    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)).
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  2. #2
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    Quote Originally Posted by paupsers View Post
    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).
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