1. 4 2 0 A-1 1 1 0 0 3 (a) Find the characteristic polynomial of A. (b) What are A's eigenvalues?...
4(b) please 4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the following matrices. 1 -2 3 1 2 (a (b) 2 6 6 2 1 13 3 -3 -5 -3 5. Diagonalize the matrix A = if possible. That is, find an invertible matrix P and 2 1 Inc.
[12 4. Find the characteristic polynomial, the eigenvalues and corresponding eigenvectors of each of the following matrices. -2 3 (a) (b) 2 3 2 6 -6 2 -1 NN 1
Let . compute (a) the characteristic polynomial (b) the eigenvalues (c) one of the corresponding eigenvectors. | 4 4 4 A = -2 -3 -6 | 1 3 6
5. Consider the matrix A-1-6-7-3 Hint: The characteristic polynomial of A is p(λ ) =-(-2)0+ 1)2. (a) Find the eigenvalues of A and bases for the corresponding eigenspaces. (b) Determine the geometric and algebraic multiplicities of each eigenvalue and whether A is diagonalizable or not. If it is, give a diagonal matrix D and an invertible matrix S such that A-SDS-1. If it's not, say why not.
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...
3 For each of the matrices below: (i) Find the characteristic polynomial (ii) Determine the eigenvalues (ii Find a basis for each eigenspace (iv) Find the algebraic and geometric multiplicities of the eigenvalues (v) Determine if the matrix is diagonalizable, and if it is, diagonalize it. -2 3 (a) A -3 2 3 For each of the matrices below: (i) Find the characteristic polynomial (ii) Determine the eigenvalues (ii Find a basis for each eigenspace (iv) Find the algebraic and...
Please circle the final answers! Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each 1 -2 0 0 A= -1 3 4 100-2) a) The characteristic polynomial is pr) = det(A - rl) = b) List all the eigenvalues of A separated by semicolons. of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them side by side in a matrix. If there are fewer than three eigenvalues, enter...
1. Consider the matrix A= 1 3 -3 (a) Find the characteristic polynomial and eigenvalues of A. (b) Find a basis for the eigenspace corresponding to each eigenvalue of A.
Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. 2 -2 7 0 3 -2 0 -1 2 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (91, 12, 13) = 1, 2, 4 the corresponding eigenvectors X1 = x X2 = X3 =
3. Let A be the matrix 1 -2 (a) What is the characteristic polynomial for A? (b) What are the eigenvalues of A? (c) What are the eigenvectors of A?