Let A be an m n matrix and let 1 be the largest singular value of A. Show that if x and y are nonzero vectors in Rn, then each of the following holds: (a) |xT Ay| _x_2 _y_2 1 [Hint: Make use of the CauchySchwarz inequality.] (b) max x_=0, y_=0 |xT Ay| _x_ _y_ = 1 4

Natural or Counting Numbers : {1,2,3,4,5,…} "0" is NOT one of them a. Natural numbers start w/ "1" and continue on to infinity Whole Numbers: {0,1,2,3,4,5...} a. Whole numbers start with "0" and continue on to infinity b. NO fractions Integers: { …-3,-2,-1,0,1,2,3...} a. These are whole numbers (0,1,2,3,…) with negative #s included Rational Numbers: any # which...