

(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 point) The matrix -1 -1 01 A = -16 0 Lk 0 has three distinct real eigenvalues if and only if -17.036 <k< 29.184
(1 point) Find the three distinct real eigenvalues of the upper-triangular matrix B= 5-7 0 0 7 -1 0 -97 -4 . 4 The eigenvalues are [Note: If there is more than one answer, separate them by commas. E.g. 1,2]
(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
(1 point) The matrix A = 1-6 1 8 k] 4 has two distinct real eigenvalues if and only if k > 24.5
(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
Solving 1. Let -Ar, A constant, with real and distinct eigenvalues 3-1 0 2-2 3 A 2 0 0 (a) Find the eigenvalues and the corresponding eigenvectors for the matrix A. (b) Use (a) to write down a fundamental matrix Φ(t) for the system z' = Az, and use Φ(t) to calculate the solution of this system that satisfies the initial condition (0)0
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....
[-5 0 5 5 0 -5 0 0 0 0 -5 0 0 0-5 0 (1 point) 2 The matrix A- has two distinct eigenvalues λ1 < λ2. Find the eigenvalues and a basis for each eigenspace. whose eigenspace has a basis of , whose eigenspace has a basis of | [1,0,0,1] Note: You can earn partial credit on this problem Preview My Answers Submit Answers Your score was recorded. You have attempted this problem 9 times. You received a...
✓ 3.32 This matrix has distinct eigenvalues. 1 2 1 6 -1 0 -1 -2 -1) (a) Diagonalize it. (b) Find a basis with respect to which this matrix has that diagonal representation. (c) Draw the diagram. Find the matrices P and P-' to effect the change of basis.
Consider a 2 x 2 matrix A that has eigenvalues 11 -2 and A2 = 5. Find the eigenvalues of A², A- and A - 21. Is the matrix A + 21 invertible? Explain. Suppose that A is a 10 x 10 matrix and that Avi V1 Av2 = 202, x = 2v1 - 02 Find real numbers a, 8 such that A’x = av. + 802