Let U be the matrix in Exercise 37. Find the distance from b = (1, 1, 1, 1, -1, -1, -1, -1) to Col U.

Data from in Exercise 37

Let U be the 8 × 4 matrix in Exercise 43 in Section 6.2. Find the closest point to y = (1, 1, 1, 1, 1, 1, 1, 1) in Col U. Write the keystrokes or commands you use to solve this problem.

Data from in Exercises 43

Show that the columns of the matrix A are orthogonal by  making an appropriate matrix calculation. State the calculation  you use.

A = -6-3 -1 2 3 6 6 -3 6 1 1-6 3-2 -3 6 -2 -1 1 2 2-12 6-1 3 3 2 2-3 1 6