Problem 2. Let P and Q be twonxn matrices and I the n x n unit matrix. Assume that p2 = P and Q? = Q. (i) Show that (P® Q)? = PQ. (1) (ii) Show that (P (I- P))? = P 8 (I – P).

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
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Problem 2.
Let P and Q be two n x n matrices and I the n x n unit
matrix. Assume that
p2 = P
and
Q² = Q.
(i) Show that
(P® Q)? = P® Q.
(1)
(ii) Show that
(P® (I - P))? = P8 (I – P).
Answerl and 2
Transcribed Image Text:Problem 2. Let P and Q be two n x n matrices and I the n x n unit matrix. Assume that p2 = P and Q² = Q. (i) Show that (P® Q)? = P® Q. (1) (ii) Show that (P® (I - P))? = P8 (I – P). Answerl and 2
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