Finding x* in the Nullspace of A: What is its Significance?

[hoffmann]

Does anyone know how to approach this problem?

Let A be an m×n matrix of rank m, where m<n. Pick a point x in R^n, and let x∗ be the point in the nullspace of A closest to x. Write a formula for x∗ in terms of x and A.

What exactly is the significance of the point x* in the nullspace of A?

 

[hoffmann]

i think this question has something to do with the orthogonality of subspaces and is analogous to saying the shortest distance between a point and an axis is just a perpendicular line...