# Math Help - Linear Transformation Question

1. ## 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.

2. 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.