Exercise 19.2.10 (Underdetermined Linear Equations) Suppose as before that A∈ Rm×n and b ∈ Rm, but m≤ n. Assume further that m= rank(A). Let U VT be the SVD of A. Argue that all solutions to Ax = b are of the form

$x = V

+UTb+V



0 y



}m

} n−m

= A+b+V2y (19.10)

for arbitrary y ∈ Rn−m, where V ≡ [ V1 m

, V2 n−m

] } n.