a= 9, b= 4, c= 5

3. Projection onto a subspace of ?: Let {ul, . .., uk} be an orthogonal basis of a subspace U in R". Define the n x n matrix Pu as 1 1 PU u 2 ului t.. . + ukuk . (a) Prove that, for any U E R", Pu UE U, and U - Pu(v) is orthogonal to any vector in U. a = 1 + fourth digit of your York student ID (b) Let b = 1 + fifth digit of your York student ID c = 1 + sixth digit of your York student ID 8 I a Compute Pu where U = span (c) Show that if U = span{u} for some non-zero vector u E R' then Pu v = proju(v). (This is one way to show that proju is a linear transformation. )