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## Homework Statement

Solve du/dt=Pu when P is a projection.

[1/2 1/2 = du/dt with

1/2 1/2]

[5 = u(0).

3]

Part of u(0) increases exponentially while the nullspace part stays fixed.

## Homework Equations

du/dt = Au with u=u(0) at t=0

## The Attempt at a Solution

I'm stuck with this problem. I was thinking that u(t)=e

^{λt}*x.

Would du/dt be considered matrix A? Thanks!