Repeat Exercise 6 using the clamped cubic splines constructed in Exercise 8.

Section 4.1 Eigenvalues and Eigenvectors Definition: Let A be an n ×n matrix, u be a nonzero n ×1 vector, and λ be a constant. If Au = λu then λ is called an eigenvalue for the matrix A and u is called the eigenvector corresponding to λ . Example: Let 35 −10 A = and u = 1 −1 −2 Find the eigenvalue, , corresponding to the eigenvector, u. Solution: Au = λu so 5 −10 −10 = λ −1 − −2 −40 −10 = λ −8 −2 λ = 4 λ Theorem: is an eigenvalue for A if and only ifA) − λI is not invertible. R