The following proposition was given in lecture without proof. Suppose we have a dataset of m examples, each with d features, x1, . . . , xm Rd. We know that satisfying the following equality is equivalent to satisfying the least squares condition. Aw = b, where A = m i=1 xixT i and b = m i=1 yixi. This can be expressed more directly in matrix form by defining A = ... ... ... x1 xm ... ... ... ... ... ... x1 xm ... ... ... T , and b = ... ... ... x1 xm ... ... ... y1 ... ym . Show that A is invertible if and only if x1, xm span Rd