The solution is given below
1-11 23 )--[-!?). - (111) DE 1 0 0 4 1 - 4 4 0-3 0 0 0 3 0 0 -1 0 5 4 2-3 E = 6. Consider the matrix A, above. Use diagonalization to evaluate A. 7. Consider the matrix B, above. Find a diagonal matrix D, and invertible matrix P, such that B = PDP- 8. Consider the matrix C, above. Find a diagonal matrix D, and invertible matrix P, such that C = PDP-!. If...
Answer 7,8,9 1-11-1)--[-13.-(41-44)--:-- 3 1 0 0 -1 0 5 4 2-3 0 0 0 6. Consider the matrix A, above. Use diagonalization to evaluate A. 7. Consider the matrix B, above. Find a diagonal matrix D, and invertible matrix P, such that BPDP-1 8. Consider the matrix C, above. Find a diagonal matrix D, and invertible matrix P, such that C = PDP-1. If this is not possible, thus the matrix is not diagonalizable, explain why. 9. Consider the...
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:...
0 0 Q2. Consider the matrix A 6 2 -5 0 1 (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)
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.
Question 5. (a) Diagonalize the matrix S = [1 0 -11 -1 2-1 and calculate A100. 1-2 0 0 (b) Diagonalize the matrix A and find a matrix B so that B2 = A. (2 007 (c) Show that the matrix H = 3 2 0 is not diagonalizable. How many linearly independent eigen- LO O 3] vectors does H have?
1 Problem 7 Let A 4 5 - 1 5 0 2 -1 2 3 -4 7 2 1 3 7 2 -4 2 0 0 10 1 1 a) (4 pts] Using the [V, DJ command in MATLAB with rational format, find a diagonal matrix D and a matrix V of maximal rank satisfying the matrix equation A * V = V * D. Is A real-diagonalizable? b) (4 pts) Write down the eigenvalues of A. For each eigenvalue,...
4 7 5 0 2 2 Problem 7 Let A= -1 2 9 -4 1 5 -1 3 7 3 1 -4 2 0 1 1 0 10 2 a) (4 pts] Using the [V, D] command in MATLAB with rational format, find a diagonal matrix D and a matrix V of maximal rank satisfying the matrix equation A * V = V * D. Is A real-diagonalizable? b) [4 pts) Write down the eigenvalues of A. For each eigenvalue,...
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3 0 7 0 3 5 [51 [51 a) Find a basis for the row space Row(A) of A (b) Find a basis for the column space Col(A) of A (c) Find a basis space d) Find the rank Rank(A) and the nullity of A (e) Determine if the vector v (1,4,-2,5,2) belongs to the null space of A. - As always,[5 is for the...
(1 point) Let A = -3 -1 6 -4 0 6 -2 -1 5 If possible, find an invertible matrix P so that D = P-1 AP is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P= D= Is A diagonalizable over R? choose Be sure you can explain why or why...