Question: problem 4: blem 4. Consider the matrix A LNN NNL a. Show that A is an orthogonal matrix. b. Find a unit vector u such

problem 4:

blem 4. Consider the matrix A LNN NNL a. Show that A is an orthogonal matrix. b. Find a unit vector u such that Au = u. c. Find a unit vector u which is perpendicular to u. What is the angle between Au and u? Why? d. Let w = ux v. What is the angle between Aw and w? e. Find the coordinates of the vectors Au, Av, and Aw with respect to the basis B = (u, v, w), and draw them in the following diagram: f. Describe the linear transformation defined by A geometrically, and find its matrix with respect to B

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