If AB = 0, the columns of B are in the nullspace of A. If those vectors are in R”, prove that rank(A) +rank(B) ≤ n.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section: Chapter Questions
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38. If AB = 0, the columns of B are in the nullspace of A. If those vectors are in R",
prove that rank(A) + rank(B) ≤ n.
Transcribed Image Text:38. If AB = 0, the columns of B are in the nullspace of A. If those vectors are in R", prove that rank(A) + rank(B) ≤ n.
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