18.06-Exercises on singular value decomposition Soved

Problem 29.1: (Based on 6.7 #4. Introduction to Linear Algebra: Strang) Verify that if we compute the  singular  value decomposition A = UΣVT of the 

Fibonacci matrix A   ,

. 

Problem 29.2: (6.7 #11.) Suppose A has orthogonal columns w1, w2, ..., wn of lengths σ1, σ2, ..., σn. Calculate AT A. What are U, Σ, and V in the SVD?