1. a) Find an orthonormal basis {v1, v2} for the vector space R3: c + y + z =
b) If u =
is any vector in R3, use the basis you found in the previous part to write an explicit formula for Projv(u1) = (u.v1)1 + (u.v2)02 in terms of a, b, c. Using this formula, find the matrix associated with the linear transformation Projv : R3 -> R3 (with respect to the canonical basis).
c Imagine that your study partner found another orthonormal basis w, w which is easier than yours for V. Surprisingly, both of you arrive at the same matrix in the previous part. Explain why.