dentify the antecedent and consequent for each conditional sentence in thefollowing statements from this book.(a) Theorem 1.3.1(a) (b) Exercise 3 of Section 1.6(c) Theorem 2.1.4 (d) The PMI, Section 2.4(e) Theorem 2.6.4 (f) Theorem 3.4.2(g) Theorem 4.2.2 (h) Theorem 5.1.7(a)

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