Q1. Let y = սլ = 1 and u2 = = > 4 3 3. Let W = Span{u1, u2}. -2 (a) Show that {ui, uz} forms an orthogonal basis for W. (b) Compute the orthogonal projection of y onto W. (c) Write y as the sum of a vector in W and a vector orthogonal to W. (d) What is the closest point to y in W? (e) Find the distance from y to W.
INSTRUCTIONS: 1. Write your work clearly and legibly. 2. You must show all your work to receive full credit; partially or completely unsupported work will receive little to no credit. 3. In your solution for each question make sure to explain: • how you go from one step to the next; mention any theorem or facts you are using. • how your work connects to the original question, and your conclusions.
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