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Mathematics, 24.04.2021 01:00 Jaymiegrimes22

Uma matriz quadrada A é considerada idempotente se A2 = A. Seja A uma matriz idempotente. (a) Mostre que I - A também é idempotente.

(b) Mostre que se A é invertível, então A = I.

(c) Mostre que os únicos autovalores possíveis de A são 0 e 1. (Dica: Suponha que x seja um autovetor com autovalor associado λ e então multiplique x à esquerda por A duas vezes.​

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