Let A be an m n matrix with singular value decomposition UVT and suppose that A

Question:

Let A be an m × n matrix with singular value decomposition U∑VT and suppose that A has rank r, where r < n. Let b ∈ Rm. Show that a vector x ∈ Rn minimizes ||b - Ax||2 if and only if
x = A+b + cr+1vr+1 + . . . + cnvn
where cr+1, . . . ., cn are scalars