Question

The matrix A is factored in the form PDP^(-1). Use Theorem 5 in Section 5.3 to...

The matrix A is factored in the form PDP^(-1). Use Theorem 5 in Section 5.3 to find the eigenvalues and corresponding eigenvectors of A.

Theorem 5 is Diagonization Theorem.

A = [3 0 0 ; -3 4 9 ; 0 0 3] = [3 0 -1 ; 0 1 -3 ; 1 0 0] [3 0 0 ; 0 4 0 ; 0 0 3] [0 0 1 ; -3 1 9 ; -1 0 3]

Semi-colons represent different rows.

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 =
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
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 #
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)= _____
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 Find the eigenvalues of A and the corresponding eigenvectors. Find a matrix P and a diagonal matrix D such thatD=P-1AP . Using the equationD=P-1AP , computeA27 .
Find all eigenvectors of this 3x3 matrix, when the eigenvalues are lambda = 1, 2, 3...
Find all eigenvectors of this 3x3 matrix, when the eigenvalues are lambda = 1, 2, 3 4 0 1 -2 1 0 -2 0 1
Find all eigenvalues and eigenvectors for the 3x3 matrix A= 1 3 2 -1 2   1...
Find all eigenvalues and eigenvectors for the 3x3 matrix A= 1 3 2 -1 2   1 4 -1 -1
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 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]
dy/dt = x- (1/2)y dy/dt =2x +3y a)matrix form b)find eigenvalues/eigenvectors c)genreal solution
dy/dt = x- (1/2)y dy/dt =2x +3y a)matrix form b)find eigenvalues/eigenvectors c)genreal solution