4. (5.A.9) Define T E L(F3) by T(21, 22, 3) (222,0, 523). Find all eigenvalues and...
Problem 3: 1-2 Let A = 1-5 1-9 -9 -10 -21 5] 7 14] Find all eigenvalues and corresponding eigenvectors.
22. Comber the matrix A-5 (a) Find all eigenvalues of the matrix A. (7 pts) (b) Find all eigenvectors of the matrix A. (8 pts) (e) Do you think that the set of the eigenwectors of A is as for the sector space Re? (Justify your answer) (5 pts)
3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that the matrix B = 0 1 is not diagonalizable. 0 4] Lo 5. Let 2, and 1, be two distinct eigenvalues of a matrix A (2, # 12). Assume V1, V2 are eigenvectors of A corresponding to 11 and 22 respectively. Prove that V1, V2 are linearly independent.
2. Find all eigenvalues and eigenvectors of the matrix 3 2 3 4
2. Find all eigenvalues and eigenvectors of the matrix 3 2 3 4
3. ( Find all eigenvalues and eigenvectors of the matrix A= [ 5 | 3 -1] and show the eigen- 1 vectors are linearly independent.
4. Find all the eigenvalues and eigenvectors of the following 3 by 3 matrix. If it is possible to diagonalized, then diagonalize the matrix. If it is not possible to diagonalize, then explain why? Show all the work. (20 points) 54 -5 A = 1 0 LO 1 1 - 1 -1
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11 1. find all eigenvalues of A, 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that K-IAK = D.
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) = {.
For all different input of x1 and x2 define F1, F2, AND F3 QUESTION 22 b b x1 . F1 F3 x2 F2 TTT AN - T.