Question

6. Let A =   3 −12 4 −1 0 −2 −1 5 −1 ...

6. Let A =   3 −12 4 −1 0 −2 −1 5 −1   . 1 (a) Find all eigenvalues of A5 (Note: If λ is an eigenvalue of A, then λ n is an eigenvalue of A n for any integer n.). (b) Determine whether A is invertible (Check if the constant term of the characteristic polynomial χA(λ) is non-zero.). (c) If A is invertible, find (i) A−1 using the Cayley-Hamilton theorem (ii) All the eigenvalues of A−1

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the characteristic polynomial of the matrix -5 4 0 0 -2 3 -1 2 0...
Find the characteristic polynomial of the matrix -5 4 0 0 -2 3 -1 2 0 (Use x instead of λ.) p(x)=
Let A, B be n × n matrices. The following are two incorrect proofs that ABhas...
Let A, B be n × n matrices. The following are two incorrect proofs that ABhas the same non-zero eigenvalues as BA. For each, state two things wrong with the proof: (i) We will prove that AB and BA have the same characteristic equation. We have that det(AB − λI) = det(ABAA−1 − λAA−1) = det(A(BA − λI)A−1) = det(A) + det(BA − λI) − det(A) = det(BA − λI) Hence det(AB − λI) = det(BA − λI), and so...
Let?= 6 3 -8 1 -2 0 0 0 -3 a. Determine the characteristic equation and...
Let?= 6 3 -8 1 -2 0 0 0 -3 a. Determine the characteristic equation and the eigenvalues of A. b. Find a basis for each eigenspace of A.
Consider the following. A = −5 12 −2 5 , P = −2 −3 −1 −1...
Consider the following. A = −5 12 −2 5 , P = −2 −3 −1 −1 (a) Verify that A is diagonalizable by computing P−1AP. P−1AP = (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n × n matrices, then they have the same eigenvalues. (λ1, λ2) =
Matrix A is given as A = 0 2 −1 −1 3 −1 −2 4 −1...
Matrix A is given as A = 0 2 −1 −1 3 −1 −2 4 −1    a) Find all eigenvalues of A. b) Find a basis for each eigenspace of A. c) Determine whether A is diagonalizable. If it is, find an invertible matrix P and a diagonal matrix D such that D = P^−1AP. Please show all work and steps clearly please so I can follow your logic and learn to solve similar ones myself. I...
Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation...
Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all (m, n) is in A, m R n ⇔ 5|(m2 − n2). It is a fact that R is an equivalence relation on A. Use set-roster notation to list the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.) ____________
Let X = {1, 2, 3, 4} and Y = {2, 3, 4, 5}. Define f...
Let X = {1, 2, 3, 4} and Y = {2, 3, 4, 5}. Define f : X → Y by 1, 2, 3, 4 → 4, 2, 5, 3. Check that f is one to one and onto and find the inverse function f -1.
Let B = {(1, 3), (?2, ?2)} and B' = {(?12, 0), (?4, 4)} be bases...
Let B = {(1, 3), (?2, ?2)} and B' = {(?12, 0), (?4, 4)} be bases for R2, and let A = 3 2 0 4 be the matrix for T: R2 ? R2 relative to B. (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [v]B and [T(v)]B, where [v]B' = [1 ?5]T. [v]B = [T(v)]B = (c) Find P?1 and A' (the matrix for T relative...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2, 4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p = Tk(R(I(q))) for some k, and find this value of k.
Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5,...
Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5, −2, 8, 1). Find the vector x that satisfies 2u − ||v||v = 3(w − 2x).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT