Q5. Consider the square matrix A 4 -3 2 (a) Show that the characteristic polynomial of...
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(4) = 12 - 91 - 2. (5 pts) (b) Compute the matrix B= AP-9A - 212. (5 pts) (e) Show that A² - 9A = 21, for the given matrix A. (5 pts) (d) Is it possible to use the equation A? - 9A = 212 to find the inverse of the given matrix A? (Justify your answer) (5 pts)
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. 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
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:...
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.
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eigenvalues and determine the determinant, (c) Compute the corresponding eigenvectors of the matrix above (a) Show that the matrix is positive definite. 1 | so that the characteristic polynomial 5 marks 0 (d) Choose a, band c in the matrix B = | 0 Based on Cayley-Hamilton's theorem, every matrix fulfills its characteristic polynomial, using the...
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)
The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. 1-3 A = 12 - 61 + 11 = 0 and by the theorem you have A2 - 64 + 1112 = 0 2 5 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 0 5 -1 -1 3 1 0 0 1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the...
- © 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.