LetA be anm X n matrix. (a) Prove thatA andA1A have the same null space. (b) Use the
Chapter 6, Problem 41(choose chapter or problem)
LetA be anm X n matrix. (a) Prove thatA andA1A have the same null space. (b) Use the rank/nullity theorem to prove that (A1A) is invertible if and only if rank{A) = n. (The relevance for us at this time is that pinv(A) = (A1At1A1 then exists if rank{A) = n.)
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