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nd a. b such that the matrix has only two eigenvalues. nd a. b such that the matrix has only two eigenvalues.
(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
A matrix has five eigenvalues, three of which are and . Find the remaining two eigenvalues. 5 X 5 We were unable to transcribe this imageWe were unable to transcribe this image
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if (1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
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=
-2 2 4 2-5 (10 pts) The matrix C 12 3 has two distinct eigenvalues. AI < has multiplicity 2 and has multiplicity -2 2 4 2-5 (10 pts) The matrix C 12 3 has two distinct eigenvalues. AI
Find the eigenvalues of the given matrices Property 2 A matrix is singular if and only if it has a zero eigenvalue 17. 21] 4t 11. Verify Property 2 for 6 A= 3 -1 2 21 7
(b) The matrix B= 1 2 2 3 3 1 3 2 4 has eigenvalues 7,2, -1. i. Find a column and a row eigenvector of B corresponding to the Perron eigenvalue. ii. Find a rank one nonnegative matrix C such that the matrix B+C will have eigenvalues 13, 2, -1. iii. Let a and B be real numbers. Calculate the eigenvalues of D(a, b) = aB+ BC. iv. Find limno(+B)"
The 2 x 2 matrix 1 = ( 43 II has two distinct real eigenvalues. 1. Give the characteristic polynomial for A in Maple notation in the form t^2 + a*t + b Characteristic polynomial = 2. Find the set of eigenvalues for A, enclosed in braces , ) with the two eigenvalues separated by a comma, like (-4, 7) Set of eigenvalues for A = 5 3. Find one eigenvector for each eigenvalue, using Maple > for vectors, e.g....
(1 point) The matrix A = 1-6 1 8 k] 4 has two distinct real eigenvalues if and only if k > 24.5
a) Evaluate the Eigenvalues and Eigenvectors of matrix A. b) Evaluate State Transition Matrix e Al using only the method of Cayley-Hamilton, et = Bol + B1A. Clearly indicate what B, and B1 are and simplify the result as much as possible. Simplify eAt as much as possible. A = []? -