Let {u 1 ..........u n } be an orthonormal basis for R n , and let 1.......... n be any real scalars. Define

Let {u₁..........u_n} be an orthonormal basis for Rⁿ, and let λ_1..........λ_n be any real scalars. Define A = λ₁u₁u₁^T+.............+ λ_nu_nu_n^T
a. Show that A is symmetric.
b. Show that λ₁,..........λ_n are the eigenvalues of A.