Linear Algebra Questions!

[QuantumJG]

Idempotent matrices. A matrix P is called Idempotent if P^2 = P. If P is idempotent and P =/= I show that detP = 0.

I don't know where to start with this!!!

Determine the Eigenvalue of A if:

A = [2 2 1; 2 5 2; 1 2 2]

and then determine the Eigenvectors.

We haven't looked at Eigenvalues or Eigenvectors yet! This is just stuff for before we look a it.

[kamil9876]

Idempotent question:

If then P is invertible.

Multiplying both sides by .





But this contradicts the hypothesis that Hence our assumption that is false and hence .

[QuantumJG]

Idempotent question:

If then P is invertible.

Multiplying both sides by .





But this contradicts the hypothesis that Hence our assumption that is false and hence .

Thanks