In the least squares problem, is the error vectorIn solving the least squares problem in class, we assumed that ATA is invertible. Prove that ATA is indeed invertible, i.e., using the assumption made in the least squares problem that the columns of A are linearly independent, prove that (ATA) 1 exists. e orthogonal to b or p or x? Show that ||e||2 equals e T b which equals b T b - p T b. This is the smallest total error E