Let A E Mmxn. (a) Suppose that x = null(A). Show that x e null(ATA) as well (b) Suppose that y e null(ATA). Show that y e null(A) as well. (c) The above two points imply that null(A) = null (ATA). In the case that the columns of A are linearly independent, use this fact to show that ATA has full rank. Let A E Mmxn. (a) Suppose that x null(A). Show that x null(ATA) as well (b) Suppose that y null(ATA). Show that y null(A) as well. (c) The above two points imply that null(A) = null (ATA). In the case that the columns of A are linearly independent, use this fact to show that ATA has full rank.