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3 -1 0 Problem 11 Let A= 16 -5 0 0 16 0 -2 15 -3 -15 2 8 0 a) [3 pts) Compute the characteristic polynomial of A and find its roots. b) [4 pts) For each eigenvalue of A find a basis for the corresponding eigenspace. c) [3 pts] Determine if A is defective. Justify your answer. d) [6 pts) If A is defective, determine the defective eigenvalue or eigenvalues, and find a Jordan chain (or set of...
Problem 11 Let A= 3 -1 0 0 16 -5 0 0 16 0 -2 15 -3 -15 2 8 a) [3 pts) Compute the characteristic polynomial of A and find its roots. b) (4 pts] For each eigenvalue of A find a basis for the corresponding eigenspace. c) [3 pts] Determine if A is defective. Justify your answer. d) [6 pts) If A is defective, determine the defective eigenvalue or eigenvalues, and find a Jordan chain (or set of...
urgent please,thanks Find all distinct (real or complex) eigenvalues of A. Then find a basis for the eigenspace of A corresponding to each eigenvalue. For each eigenvalue, specify the dimension of the eigenspace corresponding to that eigenvalue, then enter the eigenvalue followed by the basis of the eigenspace corresponding to that eigenvalue. 8 -1 9 A = -9 6 -15 |-6 4 -10 Number of distinct eigenvalues: 1 Dimension of Eigenspace: 1
Corresponding eigenvectors of each eigenvalue 9 Let 2. (as find the eigenvalues of A GA 1 -- 1 and find the or A each 5 Find the corresponding eigenspace to each eigen value of A. Moreover, Find a basis for The Corresponding eigenspace (c) Determine whether A is diagonalizable. If it is, Find a diagonal matrix ) and an invertible matrix P such that p-AP=1
7. (14 points) Let A = An eigenvalue of A is = 3. Find a basis for the eigenspace of A corresponding to 1 = 3. - [98]
4. Let E) 6 3 0 [8 Marks] 3 6 0 A = 0 0 11 a) Find the eigenvalues of A b) For each eigenvalue of A, find a basis for the corresponding eigenspace. c) Consider the linear transformation T : R3 -> R3 defined by T(x) = Ax for every xE R3. Find a basis of R3 in which the matrix representing T is diagonal
Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. A = Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. -7 16 0 1 1 005 (a) the characteristic equation of A 2+7 2–1 2–5 = 0 (1 - 5)(1 - 1)(x + 7) = 0 (b) the eigenvalues of A (Enter your answers from smallest to largest.)...
Let the matrix below act on C? Find the eigenvalues and a basis for each eigenspace in c? 1 2 - 2 1 1 2 The eigenvalues of - 2 1 (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.) are A basis for the eigenspace corresponding to the eigenvalue a + bi, where b>0, is (Type an exact answer, using radicals and i as needed.) A basis for the eigenspace...
[ 4 6 -61 Let A = -3 -4 3 . Find a basis for the eigenspace corresponding to the eigenvalue X = -2. [ 5 6 -7]
2 0 -21 3. Let A= 1 3 2 LO 0 3 (a) Find the characteristic equation of A. in Find the other (b) One of the eigenvalues for A is ) = 2 with corresponding eigenvector 1 10 eigenvalue and a basis for the eigenspace associated to it. (e) Find matrices S and B that diagonalize A, if possible.