Develop properties of rank that are sometimes needed in applications. Assume the matrix A is m
Question:
Develop properties of rank that are sometimes needed in applications. Assume the matrix A is m × n.
Show from parts (a) and (b) that rank AB cannot exceed the rank of A or the rank of B. (In general, the rank of a product of matrices cannot exceed the rank of any factor in the product.)
a. Show that if B is n × p, then rank AB ≤ rank A.
b. Show that if B is n × p, then rank AB ≤ rank B.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
Question Posted: