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Linear Algebra Questions!

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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:

--- Quote from: kamil9876 on September 15, 2009, 08:38:29 pm ---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 .



--- End quote ---

Thanks

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