Question

Suppose that a 4 × 4 matrix A has eigenvalues ?1 = 1, ?2 = ?...

Suppose that a 4 × 4 matrix A has eigenvalues ?1 = 1, ?2 = ? 2, ?3 = 4, and ?4 = ? 4. Use the following method to find det (A).

If

p(?) = det (?I ? A) = ?n + c1?n ? 1 + ? + cn

So, on setting ? = 0, we obtain that

det (? A) = cn or det (A) = (? 1)ncn

det (A) =

Math   Algebra   
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
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...
2 1 1 1 0 1 1 1 0 These questions have got me confused: 1....
2 1 1 1 0 1 1 1 0 These questions have got me confused: 1. By calculation, I know this matrix has eigenvalue -1, 0, 3 and they are distinct eigenvalues. Can I directly say that this matrix is diagonalizable without calculating the eigenspace and eigenvectors? For all situations, If we get n number of answers from (aλ+b)n , can we directly ensure that the matrix is diagonalizable? 2. My professor uses CA(x)=det(λI-A) but the textbook shows CA(x)=det(λI-A). which...
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]
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
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
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?
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
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)= _____
find the eigenvalues of the following matrix. then find the corresponding eigenvector(s) of one ofthose eigenvalues...
find the eigenvalues of the following matrix. then find the corresponding eigenvector(s) of one ofthose eigenvalues (pick your favorite). 1 -2 0 -1 1 -1 0 -2 1
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT