Calculate 2D matrix using the unitary group

[tazzzdo]

It's problem #5 on this homework set: https://docs.google.com/open?id=0B9c8sp75B5ZRMHAxYXB3MWdhYk0

I can calculate ($\pi$/4)(n₁σ₁ + n₂σ₂ + n₃σ₃) easily, but I have NO clue how a matrix M = exp[($\pi$/4)(n₁σ₁ + n₂σ₂ + n₃σ₃)].

 

[tazzzdo]

If each σ is diagonal or anti-diagonal, could I just write each diagonal entry of exp(σ) as e^σ_ij, then add all of the σ's up? Like this case:

http://en.wikipedia.org/wiki/Matrix_exponential#Diagonalizable_case