Linear Algebra and Its Applications · Problem 2.4.6

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

Suppose

A

is an

m

n

matrix of rank

r

. Under what conditions on those numbers does (a)

A

have a two-sided inverse:

AA^{-1} = A^{-1}A = I

? (b)

Ax = b

have infinitely many solutions for every

b