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Math Help - Linear Transformation Question

  1. #1
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    Linear Transformation Question

    I am having trouble proving the following statement:

    Let V be a n-dimensional vector space with an ordered basis \beta. Prove that T:V \rightarrow F^n by T(x) = [T]_{\beta} is linear.
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  2. #2
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    So far I have:

    \beta= { u_1,u_2,...,u_n} and a_1,a_2,...,a_n are unique scalars.

    x = \sum ^{n}_{i=1}a_{i}u_{i}

    T(x) = T(\sum ^{n}_{i=1}a_{i}u_{i}) = \sum ^{n}_{i=1}a_{i}T(u_{i})

    I'm not sure if this is correct.
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