# Math Help - Find an invertible matrix P

1. ## Find an invertible matrix P

Let $T:R^4 --> R^4$be a linear transformation T(v) = Av where A =

[1 1 3 1]
[0 2 2 4]
[0 0 3 2]
[0 0 1 4]

Find the characteristic polynomial of A and compute the eigenvalues of T. Find a basis for each eigenspace. Either find an invertible matrix P and a disgonal matrix D such that $P^{-1}AP = D$or else explain why this is impossible.

I know how to find the characteristic polynomial and the eigenvalues of A but not T.

2. The eigenvalues of $A$ are exactly the eigenvalues of $T$. Indeed, if $T(v) = Av =\lambda v$ then $T(v) = \lambda v$.