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Math Help - another linear algebra question I can't get

  1. #1
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    another linear algebra question I can't get

    suppose that V is finite dimensional, with dimV=n. Prove that there exist one-dimensional subspaces U1,...,Un (1 and n are supposed to be subscripts)of V such that

    V = U1 + ... + Un (again, 1 and n are subscripts and + denotes a direct sum)
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  2. #2
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    Quote Originally Posted by alexmin View Post
    suppose that V is finite dimensional, with dimV=n. Prove that there exist one-dimensional subspaces U1,...,Un (1 and n are supposed to be subscripts)of V such that

    V = U1 + ... + Un (again, 1 and n are subscripts and + denotes a direct sum)
    If \mbox{dim}(V) = n it means it has a basis \bold{v}_1,...,\bold{v}_n. Let U_i = \mbox{span}(\bold{v}_i) then U_1+...+U_n = V.
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