Question

the question 7.1.17 along with the textbook solution is above, however part (c) and (b) make little sense to me

7.1.17. Suppose that {λί, λ2, ,Ad are the eigenvalues for Anem and let (Ak, c be a particular eigenpair. σ (A), explain why (A_ÀI)-ic-c/(λ-A) (a) (b) For an arbitrary vector dnx, prove that the eigenvalues of For λ A+cd" agree with those of A except that λ, is replaced by A+ cdr and A agree except that λ, is replaced by a specified (c) How can d be selected to guarantee that the eigenvalues of number Use (62.3) to compute the characteristic polynomial for A + ed to be det (A + cd"-AI)-det (A-λ1 + cd") det (A-11) (1 + dT(A-λ1) ic) d? i/k The roots of this polynomial are λ, . . . Ak-1, Ak + dTC, Ak + i, . . . , λη. (μ-λ)c will do the job.

Answer 1

det (A-A 1)-t(A4) 2.

ㄒ c..C