Suppose A is an m × n matrix and B is an n x p matrix. Show that Col ABC Col A and NulBC Nul AB. Hence, rank (AB) ≤ rank A and rank (AB) ≤ rank B.
Suppose A is an m × n matrix and B is an n x p matrix. Show that Col ABC Col A and NulBC Nul AB. Hence, rank (AB) ≤ rank A and rank (AB) ≤ rank B.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose A is an m × n matrix and B is an n × p matrix. Show that
Col ABC Col A and Nul B C Nul AB.
Hence, rank (AB) ≤ rank A and rank (AB) ≤ rank B.
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