You can start by choosing a basis for , and then complete it to a basis of .

The first column of the matrix of T with respect to this basis is the coordinates of T(w_1) expressed in this basis: Writing

the first column of the matrix consists of the numbers

But is an invariant subspace of , so since is a member of , then will also be a member of . But this means that can be expressed in the basis of , so that all the scalars are . In conclusion, the last entries in the first column of the matrix are 0.

Repeat this procedure for all the basis vectors to see that for each of the first columns, it is the case that the last entries are 0.