Finding the formula of a projection in M2x2 (R)

benlinus

1. The problem statement, all variables and given/known data

Let T : M_2x2(ℝ) → M_2x2(ℝ) denote the projection on W along U.

W={
[a b]
[c d] : a+b+c+d=0 }

U= span{ I₂ }

Find the matrix representation of T with respect to the standard basis of M_2x2(ℝ) and the formula for T.

2. Relevant equations

From my notes, I know W is the range of T and U is the kernel of T.

M_2x2(ℝ) = W [itex]\oplus[/itex] U (Direct sum)

3. The attempt at a solution

I am unsure how to proceed. Any thoughts?