Linear Algebra and Its Applications · Problem 2.4.27

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

(Important)

A

is an

m

n

matrix of rank

r

. Suppose there are right-hand sides

b

for which

Ax = b

has no solution. (a) What inequalities (

<

\leq

) must be true between

m

n

, and

r

? (b) How do you know that

A^T y = 0

has a nonzero solution?