Question

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) =

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
the Markov chain on S = {1, 2, 3} with transition matrix p is 0 1...
the Markov chain on S = {1, 2, 3} with transition matrix p is 0 1 0 0 1/2 1/2; 1/2 0 1/2 We will compute the limiting behavior of pn(1,1) “by hand”. (A) Find the three eigenvalues λ1, λ2, λ3 of p. Note: some are complex. (B) Deduce abstractly using linear algebra and part (A) that we can write pn(1, 1) = aλn1 + bλn2 + cλn3 for some constants a, b, c. Don’t find these constants yet. (C)...
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...
Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. 0 −3 5...
Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. 0 −3 5 −4 4 −10 0 0 4 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (λ1, λ2, λ3) = the corresponding eigenvectors x1 = x2 = x3 =
We say two n × n matrices A and B are similar if there is an...
We say two n × n matrices A and B are similar if there is an invertible n × n matrix P such that A = PBP^ -1. a) Show that if A and B are similar n × n matrices, then they must have the same determinant. b) Show that if A and B are similar n × n matrices, then they must have the same eigenvalues. c) Give an example to show that A and B can be...
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...
The matrix [−1320−69] has eigenvalues λ1=−1 and λ2=−3. Find eigenvectors corresponding to these eigenvalues. v⃗ 1=...
The matrix [−1320−69] has eigenvalues λ1=−1 and λ2=−3. Find eigenvectors corresponding to these eigenvalues. v⃗ 1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ and v⃗ 2= ⎡⎣⎢⎢ ⎤⎦⎥⎥ Find the solution to the linear system of differential equations [x′1 x′2]=[−13 20−6 9][x1 x2] satisfying the initial conditions [x1(0)x2(0)]=[6−9]. x1(t)= ______ x2(t)= _____
5. Given A = | 0 2 5 1 0 3 1 0 0 |. (a)...
5. Given A = | 0 2 5 1 0 3 1 0 0 |. (a) Find the characteristic equation of A. (b) Compute eigenvalues of A. (c) Find an eigenvector corresponding to each of the eigenvalues found in part (b).
3. Diagonalize the matrix J by computing P, D, and P −1 . J = "...
3. Diagonalize the matrix J by computing P, D, and P −1 . J = " 1 3 −1 5# 4. Find the eigenvalues and eigenvectors of the following matrix. W = " 7 −9 4 7 #
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...
Consider the recurrence relation T(1) = 0, T(n) = 25T(n/5) + 5n. (a) Use the Master...
Consider the recurrence relation T(1) = 0, T(n) = 25T(n/5) + 5n. (a) Use the Master Theorem to find the order of magnitude of T(n) (b) Use any of the various tools from class to find a closed-form formula for T(n), i.e. exactly solve the recurrence. (c) Verify your solution for n = 5 and n = 25.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT