3. (4 points) Find the eigenvalues of A25, where A 0-1 Hint: If A is an...
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).
Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positive definite. Determine the values of β for which the matrix A is positive semidefinite. (c) For each eigenvalue of A, find a basis for the corresponding eigenspace. (d) Find an orthonormal basis for R3 consisting of eigenvectors of...
Find the eigenvalues and number of independent eigenvectors. (Hint: 4 is an eigenvalue.) 10 -6 12 -8 0 0 | 12 -7 -1 a) Eigenvalues: 4,4, -1; Number of independent eigenvectors: 2 b) Eigenvalues: 4,2, -1; Number of independent eigenvectors: 3 c) Eigenvalues: 4,-2,1; Number of independent eigenvectors: 3 d) Eigenvalues: 4,-2, -1; Number of independent eigenvectors: 3 e) Eigenvalues: 4,-2, -2; Number of independent eigenvectors: 2 f) None of the above.
please solve all 3 Differential Equation problems 3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)-0 (a) Show that λ =0 is not an eigenvalue (b) Show that the eigenfunctions are the functions {sin α11,o, where αη įs the nth positive root of the equation tan z -z (c) Draw a sketch indicating the roots as the points of intersection of the curves y tan z and y...
30 01 1. Let A-0 3 4 0 4 3] (a) Find the eigenvalues and their corresponding eigenspaces for A. (b) Is A diagonalisable? If so, find a diagonalisation for A. (c) Find a formula for A" where n is any positive integer
4 0 2 7) Find the eigenvalues of the matrix A= 1-2 3-4 0 0 - Clearly show your work. (15 points) 3
5. (a) (10 pts) Find the eigenvalues of A= 4 -5 8 0 3 0 -1 3 -2 (b) (6 pts) Find a basis for any one of eigenspaces of A (you may use any eigenvalue you have found in (a)).
AB 31) Find the eigenvalues and eigenspaces of the matrix-4 0 4 Hint: One way to simplify 6 -2-3 a term of the form a +bi, where a and b are real numbers, is to multiply it by a -bi
matrix algebra 14. 0/3 points | Previous Answers HoltLinAlg2 6.1.067. Consider the matrix A 00-2-11 1 1 7 6 A=12041 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) Find a basis for each eigenspace. 0 (smaller eigenvalue) (larger eigenvalue) 14. 0/3 points | Previous Answers HoltLinAlg2 6.1.067. Consider the matrix A 00-2-11 1 1 7 6 A=12041 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) Find a basis for each eigenspace. 0...
[1 3 1 1 Find the eigenvalues of A = Calculate the algebraic 0 -1 1 2 0 0 2 - 2 0 0 0 multiplicity of each eigenvalue. 1 The matrix A = -1 0 3 0 -3 has eigenvalues ! 0 - 1 -2 and 12 = 0.