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## Homework Statement

Find a basis for V.

Let W be a vector space of dimension 4. Let beta = {x1, x2, x3, x4 } be an ordered basis for W. Let V = {T in L(W) | T(x1) + T(x2) = T(x4) }

## Homework Equations

L(W) is the set of linear transformations from W to W

## The Attempt at a Solution

We know that V has dimension 3, since T(x4) can be expressed in terms of T(x1) and T(x2). So V has the general form of {T(x1), T(x2), T(x3), T(x1) + T(x2)}

But I'm lost as to how I can find a basis for V when nothing is said explicitly.