Linear Transformation Question

**lllll** · February 5th 2008, 10:42 PM

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.

**lllll** · February 6th 2008, 11:23 AM

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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