Question 4: Suppose that A is a 2 x 2 matrix and Find A? Hint: The...
# 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...
linear algebra
3. Suppose that A is a 2 x 2 matrix: (a) Find Az if r = (13) is an eigenvector with eigenvalue 1 = 3. (b) Is it possible for A to have 3 eigenvalues? Why or why not? (C) True/False: If is an eigenvalue of A, there are infinitely many eigenvectors with eigenvalue .. (d) True/False: If I = 0) is an eigenvalue, then Eo = Nul (A).
Find the matrix A that has the given eigenvalues and
corresponding eigenvectors.
Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A=
Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A=
Suppose A is a symmetric 3 by 3 matrix with eigenvalues 0, 1, 2 (a) What properties 4. can be guaranteed for the corresponding unit eigenvectors u, v, w? In terms of u, v, w describe the nullspace, left nullspace, (b) row space, and column space of A (c) Find a vector x that satisfies Ax v +w. Is x unique? Under what conditions on b does Ax = b have a solution? (d) (e) If u, v, w are...
please solve them clear
Q1. Let A= be a 2 x 2 matrix. 45 (a) Find the characteristic polynomial of the matrix A. (5 pts) (b) Find all eigenvalues and associated eigenvectors of the matrix A. (10 pts) (c) If X is an eigenvalue of A, what do you think it would be the eigenvalue of the matrix 5A?(Justify your answer) (5 pts) Q2. Consider the matrix A = 2 -5 -6 1-50 (a) Find all eigenvalues of the matrix...
Problem 1. (2 points) Find a 2 x 2 matrix A such that [-] and are eigenvectors of A with eigenvalues 9 and 3, respectively. A=
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).
Find the eigenvalues and eigenvectors of the matrix A - = -3 10 2 —4
Consider the 3 x 3 matrix A defined as follows 7 4-4 a) Find the eigenvalues of A. Is A singular matrix? b) Find a basis for each eigenspace. Then, determine their dimensions c) Find the eigenvalues of A10 and their corresponding eigenspaces. d) Do the eigenvectors of A form a basis for IR3? e) Find an orthogonal matrix P that diagonalizes A f) Use diagonalization to compute A 6
[18 Point Problem 5: Consider the following (2 x 2) matrix A: 1-4 -1] A= 13 2 a) Find the eigenvalues and the eigenvectors for the matrix. b) Compute the magnitude of the eigenvectors corresponding to both eigenvalues where a = 1. Observing your results, what conclusion can you draw. ('a' is the complex number replacing the free variables 11 or 12)