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5. (a) (10 pts) Find the eigenvalues of A= 4 -5 8 0 3 0 -1 3 -2 (b) (6 pts) Find a basis for any one of eigenspaces of A (you may use any eigenvalue you have found in (a)).
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is diagonalizable. Show that it is, in fact, diagonalizable, and find C and D such that C (you may make this as trivial as you wish!) AC = D 5.(5 pts) Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is NOT diagonalizable. Show WHY it is not diagonalizable. 6. (5 pts) Let T:...
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 3 2 6 1 -2 3 L6 4 12 b) Find the Fourier series representation of the function with period 21 given by t2 0 <t<TE i < t < 270 f(t) = {.
Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix (3 2 6 1 -2 3 16 12 b) Find the Fourier series representation of the function with period 2 given by +2 ost < ist <2x f(t) = {. 2 ºs!<
-2 2 4 2-5 (10 pts) The matrix C 12 3 has two distinct eigenvalues. AI < has multiplicity 2 and has multiplicity
-2 2 4 2-5 (10 pts) The matrix C 12 3 has two distinct eigenvalues. AI
0 6 5 14. The eigenvalues of | 1 4-4 | are: λί = λ2 =-2, λ3 =-1. The number of X2- 2 10 -9 independent eigenvectors is (a) 1, (b) 2, (c) 3, (d) 4, (e) None of the above 15. The eigenvalues of 4 | are: λί-3, λ2-Ag=-2. Which of the following is not an eigenvector: (a)(b)4((1 0 (e) Each of these is an eigenvector.
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5. (a) (10 pts) Find the eigenvalues of 6 0 -1 A= -5 20 -12 0 2 (b) (6 pts) Find a basis for any one of eigenspaces of A (you may use any eigenvalue you have found in (a)).
5. (a) (10 pts) Find the eigenvalues of A= 6 0 -5 2 12 0 0 2 (b) (6 pts) Find a basis for any one of eigenspaces of A (you may use any eigenvalue you have found in (a)).
linear algebra no calculator please
5. (a) (10 pts) Find the eigenvalues of 6 0 -1 A= -5 20 -12 0 2 (b) (6 pts) Find a basis for any one of eigenspaces of A (you may use any eigenvalue you have found in (a)).
5. (a) (10 pts) Find the eigenvalues of 6 0-11 -5 20 -12 0 2 (b) (6 pts) Find a basis for any one of eigenspaces of A (you may use any cigenvalue you have found in (a)).