[1 3 1 1 Find the eigenvalues of A = Calculate the algebraic 0 -1 1...
Find a basis for each eigenspace and calculate the geometric multiplicity of each eigenvalue. 3 2 The matrix A = 0 2 0 has eigenvalues X1 = 2 and X2 1 2 3 For each eigenvalue di, use the rank-nullity theorem to calculate the geometric multiplicity dim(Ex). Find the eigenvalues of A = 0 0 -1 0 0 geometric multiplicity of each eigenvalue. -7- Calculate the algebraic and
Find the eigenvalues and their eigenvectors and eigenspace for each matrix listed below. If the algebraic multiplicity of a eigenvalue is greater than one, nd the geometric multiplicity as well for that eigenvalue. (There are C and D). 3
(1 point) Suppose a 3 x 3 matrix A has only two distinct eigenvalues. Suppose that tr(A) = 1 and det(A) = 63. Find the eigenvalues of A with their algebraic multiplicities. The smaller eigenvalue has multiplicity and the larger eigenvalue has multiplicity
question about linear algebra 1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as an eigenvalue with algebraic multiplicity 1. The eigenvalue -2 has an associated eigenvector The eigenvalue 4 has an associated eigenvector 1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as...
Question 1: Question 2: Thx, will give a thumb Determine the algebraic and geometric multiplicity of each eigenvalue of the matrix. 2 3 3 3 2 3 3 3 2 Identify the eigenvalue(s). Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is one distinct eigenvalue, 1 = OB. There are two distinct eigenvalues, hy and 12 (Use ascending order.) OC. There are three distinct eigenvalues, 14 , 22 = (Use...
3 1. Let A = 0 (a) Compute the eigenvalues of A and specify their algebraic multiplicities. (b) For every eigenvalue 1, determine the eigenspace Ex and specify its dimension. (c) Is A a defective matrix? Why or why not? (d) Is A a singular matrix? Why or why not? (e) Determine the eigenvalues of (74) + 5.
[2 1 37 A = 0 3 2 To o 2 a) Find the eigenvalues of A. b) Find algebraic multiplicity of each eigenvalues of A. Bonus Find geometric multiplicity of each eigenvalues of A.
Q1) Let A = 2 0 0 1 3 -1 2 2 a) Determine all eigenvalues of A. b) Determine the basis for each eigenspace of A c) Determine the algebraic and geometric multiplicity of each eigenvalue.
(1 point) The matrix 4-4 A 0 -8 0 4 has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace The eigenvalue A, is and a basis for its associated eigenspace is The eigenvalue A2 is and a basis for its associated eigenspace is
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).