Can anyone explain how they got these answers? [Questions](https://i.stack.imgur.com/jaFTF.png)

In #4, my confusion is this: the prior problems involve the eigenvalues via the diagonalization, so not being able to do that leaves me confused.

In #5... I don't see the trick. There's a prior problem where P determined the coefficients and e^(lambda t) and D determined the lambdas, but this appears to do neither (that doesn't correspond to the answer given).