Question

4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is diagonalizable. Show that it is, in fact,
0 0
Add a comment Improve this question Transcribed image text
Answer #1

2 A = C AC A Thun elanoutemstic prlyno miał of (A-2) (p A iS C O G C o O -5 mimimel pohgomial fAis (2-3) Trinigmal pohynowmic

Add a comment
Know the answer?
Add Answer to:
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • # 2: Consider the real symmetric matrix A= 4 1 a) What are the eigenvalues and...

    # 2: Consider the real symmetric matrix A= 4 1 a) What are the eigenvalues and eigenvectors. [Hint: Use wolframalpha.] b) What is the trace of A, what is the sum of the eigenvalues of A. What is a general theorem th c) The eigenvalues of A are real. What is a general theorem which assert conditions that t d) Check that the eigenvectors are real. What is a general theorem which asserts conditions th asserts equality? eigenvalues are real...

  • 4. True/False.As always, give a brief explanation for your answer, if true, why true, or if...

    4. True/False.As always, give a brief explanation for your answer, if true, why true, or if false what would make it true, or a counterexample - 2 pts each: a. If Spanv v, V}) = Span({w,W)= W , then W is 2-dimensional. b. The kernel of a linear transformation T: R8 -R5 cannot be trivial c. If A is an invertible matrix, then A is diagonalizable 0, then A cannot be full-rank d. If det(A) e. If A is an...

  • Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 3 2 6 1...

    Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 3 2 6 1 -2 3 L6 4 12 b) Find the Fourier series representation of the function with period 21 given by t2 0 <t<TE i < t < 270 f(t) = {.

  • 0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3,...

    0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.

  • 2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A ...

    2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A is, or is NOT, diagonalizable. (b Explain why A is, or is NOT, inzertibie. 2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A is, or is NOT, diagonalizable. (b Explain why A is, or is NOT, inzertibie.

  • Suppose A is a 3 by 3 matrix. Decide if the matrix is diagonalizable given the...

    Suppose A is a 3 by 3 matrix. Decide if the matrix is diagonalizable given the following information: A has two distinct eigenvalues 11, 12 whose eigenspaces are a line and a plane, respectively. Not diagonalizable Not enough information O Diagonalizable Question 14 6 pts READ FIRST: Fill in the blanks. ADDITIONALLY, on you scanned work, show how you arrive at your answers. (Your answer must match your work or you will receive no credit.) The set S= {(1,-1,3), (-3,4,9),...

  • 3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that...

    3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that the matrix B = 0 1 is not diagonalizable. 0 4] Lo 5. Let 2, and 1, be two distinct eigenvalues of a matrix A (2, # 12). Assume V1, V2 are eigenvectors of A corresponding to 11 and 22 respectively. Prove that V1, V2 are linearly independent.

  • 16. Assume that M is a 4 x 4 matrix with eigenvalues 11 = -1, 12...

    16. Assume that M is a 4 x 4 matrix with eigenvalues 11 = -1, 12 = 0, 13 = 5, y = 1. Choose the correct answer(s) (a) A basis of R* can be formed using eigenvectors of M (b) The matrix M is nonsingular c) The matrix M is diagonalizable (d) All of the above 17. Let S be a 3 x 3 symmetric matrix whose eigenvalues are 12 = 4, 13 = -1. Choose the correct answer(s)...

  • 7.4. Let A be a 2 x 2 matrix which is not equal to diagonal matrix....

    7.4. Let A be a 2 x 2 matrix which is not equal to diagonal matrix. Show that A is diagonalizable if and only if it has 2 distinct eigenvalues li # 12. 7.5. Suppose that f :R3 R3 is a linear transformation. Suppose that f(vi) = TV, f(V2) = 1984v2 and f(03) = 03, for nonzero vectors V1, V2 and 03. Determine if f is an isomorphism.

  • 4 7 5 0 2 2 Problem 7 Let A= -1 2 9 -4 1 5...

    4 7 5 0 2 2 Problem 7 Let A= -1 2 9 -4 1 5 -1 3 7 3 1 -4 2 0 1 1 0 10 2 a) (4 pts] Using the [V, D] command in MATLAB with rational format, find a diagonal matrix D and a matrix V of maximal rank satisfying the matrix equation A * V = V * D. Is A real-diagonalizable? b) [4 pts) Write down the eigenvalues of A. For each eigenvalue,...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT