5. Show that equation (2) defines an inner product on Rmx. 2. Let x = (1,...

  

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5. Show that equation (2) defines an inner product on Rmx. 2. Let x = (1, 1, 1, 1) and y = (8, 2, 2, 0). (a) Determine the angle between x and y. (b) Find the vector projection p of x onto y. (c) Verify that x-p is orthogonal to p. (d) Compute |x-P2, P2, x2 and verify that the Pythagorean law is satisfied. 5. Show that equation (2) defines an inner product on Rmx. 2. Let x = (1, 1, 1, 1) and y = (8, 2, 2, 0). (a) Determine the angle between x and y. (b) Find the vector projection p of x onto y. (c) Verify that x-p is orthogonal to p. (d) Compute |x-P2, P2, x2 and verify that the Pythagorean law is satisfied.