Q5. Consider the square matrix A = [] (a) Show that the characteristic polynomial of A...
Q5. Consider the square matrix A - 6 4 3 (a) Show that the characteristic polynomial of A# (X) = x-91-2. (6 pts) (b) Compute the matrix B-A 9A 21. (5 pts) (c) Show that A2 9A-21, for the given matrix A. (5 pts) (d) Is it possible to use the equation A? (Justify your answer) (5 pts) 9A 21, to incl the inverse of the given matrix A
Q5. Consider the square matrix A = (a) Show that the characteristic polynomial of A is: p(A) = 12 - 82-3. (5 pts) (b) Compute the matrix B-A? - SA - 3/2 (5 pts) (c) Show that A? - 8A - 3/2 for the given matrix A. (5 pts) (d) Is it possible to use the equation A? - 8A = 37, to find the inverse of the given matrix A? (Justify your answer) 5 pts)
Q5. Consider the square matrix A 4 -3 2 (a) Show that the characteristic polynomial of A is: p(x) = 12 – 61 – 7. (b) Compute the matrix B= A2 – 6A – 712. (c) Show that A² – 6A = 712 for the given matrix A. (d) Is it possible to use the equation A2 – 6A = 712 to find the inverse of the given matrix A? (Justify your answer)
solve it clear please ????? 6 0 0 1 Q2. Consider the matrix A = 2 -5 -6 -50 (a) Find all eigenvalues of the matrix A. (7 pts) (b) Find all eigenvectors of the matrix A. (8 pts) (c) Do you think that the set of the eigenvectors of A is a basis for the vector space R$? (Justify your answer) (5 pts) Q5. Consider the square matrix A = (a) Show that the characteristic polynomial of A is:...
Q5. Contudes the square matrix A- (a) Show that the characterbtie polynomial of A la p(A) = 42-81-3. (5 pts) (1) Compute the matrix - A-84-3) (pt) (C) Show that A? - 8A - 3; for the given matrix A. (5 pts) (d) Is it possible to use the equatice AP-8A = 31to find the inverse of the given matrix A? (Justify your answer) (5 pts
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.
Q1. Let A = be a 2 x 2 matrix. 30 (a) Find the characteristic polynomial of the matrix A. (5 pts) (b) Find all eigenvalues and associated eigenvectors of the matrix A. (10 pts) (c) If is an eigenvalue of A, what do you think it would be the eigenvalue of the matrix 7A?(Justify your answer) (5 pts)
Find the characteristic polynomial of matrix A. (II) Find eigenvalues of the matrix A. Consider matrices 2 A= 2 -4 1 and -8 12 -2 3
- © consider the companion form matrix a) b) show its characteristic polynomial is Pa () = 1 +2, ++24+24 show if a; is an eigenvalue of A, then (x 1; 1; 1) is the corresparling eigenvector.
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...