Question

Q‒5. [8+4+8 marks] Let Find the eigenvalues of A and the corresponding eigenvectors. Find a matrix...

Q‒5. [8+4+8 marks] Let

  1. Find the eigenvalues of A and the corresponding eigenvectors.
  2. Find a matrix P and a diagonal matrix D such thatD=P-1AP .
  3. Using the equationD=P-1AP , computeA27 .

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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 =
4. Let A = [-5 -5] [5 -5] a. Find the eigenvalues and eigenvectors for A....
4. Let A = [-5 -5] [5 -5] a. Find the eigenvalues and eigenvectors for A. b. Find an invertible matrix P and a matrix C of the form [a -b] such that A=PCP-1. [b a] c. For the transformation given by T(x) = Ax find the scaling factor and the angle of rotation.
Find the eigenvalues and the eigenvectors corresponding to them of the matrix -2 1 3 0...
Find the eigenvalues and the eigenvectors corresponding to them of the matrix -2 1 3 0 -2 6 0 0 4
Suppose A ∈ Rk×k is symmetric. Find the eigenvalues and corresponding eigenvectors for A + cIk...
Suppose A ∈ Rk×k is symmetric. Find the eigenvalues and corresponding eigenvectors for A + cIk where Ik ∈ Rk×k is the identity matrix and c ∈ R is a constant
Normally, we start with a matrix and find the eigenvalues and eigenvectors. But it’s interesting to...
Normally, we start with a matrix and find the eigenvalues and eigenvectors. But it’s interesting to see if this process can be performed in reverse. Suppose that a 2x2 matrix has eigenvalues of +2 and -1 but no info on the eigenvectors. Can you find the matrix? How many matrices would have these eigenvalues?
Normally, we start with a matrix and find the eigenvalues and eigenvectors. But it’s interesting to...
Normally, we start with a matrix and find the eigenvalues and eigenvectors. But it’s interesting to see if this process can be performed in reverse. Suppose that a 2x2 matrix has eigenvalues of +2 and -1 but no info on the eigenvectors. Can you find the matrix? How many matrices would have these eigenvalues?
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)= _____
Complex Eigenstuff Compute the eigenvalues and eigenvectors for the given matrix A. List the eigenvalues so...
Complex Eigenstuff Compute the eigenvalues and eigenvectors for the given matrix A. List the eigenvalues so the first one has negative imaginary part. Write the corresponding eigenvectors in the form [u+iv1]. If there is only one eigenvector, leave the entries for the second eigenvalue and eigenvector blank. A=[4 -3 3 4]
Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A...
Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R^m. Note that this means (in this case) that the eigenvectors are distinct and form a base of the space.
find all eigenvalues and eigenvectors of the given matrix A= [3 2 2 1 4 1...
find all eigenvalues and eigenvectors of the given matrix A= [3 2 2 1 4 1 -2 -4 -1]
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT