Suppose that a matrix A has the characteristic polynomial (1+1)3 (a 1 + 12 + b)...
Problem #30: [2 marks] Suppose that a matrix A has characteristic polynomial p() = 1 - 31' + 814 - 23. Consider the following statements. (i) i = 2 is an eigenvalue of A. (ii) A is a 4 x 4 matrix. (iii) That same p() is also the characteristic polynomial of A! Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True...
please do both 1 & 2 () There is interesting relationship2 between a matrix and its characteristic equation that we explore in this exercise. 2 (a) We first illustrate with an example. Let B - 1 -2 i. Show that 2-4 is the characteristic polynomial for B ii. Calculate B2. Then compute B2+ B 412. What do you get? (b) The first part of this exercise presents an example of a matrix that satisfies its own characteristic equation. Explain for...
Find the characteristic polynomial, the eigenvalues and a basis of eigenvectors associated to each eigenvalue for the matrix 1 A= = 66 -2) a) The characteristic polynomial is p(r) = det(A – r1) = b) List all the eigenvalues of A separated by semicolons. 1;-2 c) For each of the eigenvalues that you have found in (b) (in increasing order) give a basis of eigenvectors. If there is more than one vector in the basis for an eigenvalue, write them...
Find the characteristic polynomial and the eigenvalues of the matrix. 3 1 -15 The characteristic polynomial is (Type an expression using à as the variable. Type an exact answer, using radicals as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The real eigenvalue(s) of the matrix is/are (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Type each answer only once.) OB. The...
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
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?
Consider the matrix A. [ 300 A = 120 L-6 7 -1 Find the characteristic polynomial for the matrix A. (Write your answer in terms of .) Find the real eigenvalues for the matrix A. (Enter your answers as a comma-separated list.) A= Find a basis for each eigenspace for the matrix A. (smallest eigenvalue) (largest eigenvalue)
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.
1. Consider the matrix (a) Find the characteristic polynomial and eigenvalues of A (b) Find a basis for the eigenspace corresponding to each eigenvalue of A. (c) Find a diagonalization of A. That is, find an invertible matrix P and a diagonal matrix such that A - POP! (d) Use your diagonalization of A to compute A'. Simplify your answer.
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...