Consider the following. 01-3 -5 2 0 1 2 2 6 -2 4 (a) Verify that A is diagonalizable by computing P1AP. (b) Use the result of part (a) and the theorem below to find the eigenvalues of A Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (A1, λ2, A3) Nood Holn2
(4 points) 3 3 -2 Find the LU factorization of the 3 x 3 matrix A3 5 6 -12 20 22 and use it to solve the system 13 #2 | = 1-23 -88 T1 3 5 6 12 20 22 C3
9. Given det(A5x5)-3, find det(A3), det(5A), det(2AT), det(3A-1).
9. Given det(A5x5)-3, find det(A3), det(5A), det(2AT), det(3A-1).
1 A= Find A1017 and Justify your answer 1 ✓2 B = O 01 3 Find B” and Justify your answer. 0 3
if A3 = 22.5 and A13 = 1,328,602.5 Find An There are 3 possible answers!
Linear algebra question
01 -3 -1 3 4 -6 8 0 -1 31 2. Find a basis for the image of the matrix A-
Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-equivalent to A, where 1 0 1 0 1 0 1 -2 0 5 0 0 01 3 (a) Find: the rank of A the dimension of the nullspace of A (b) Find a basis for the nullspace of A. Enter each vector in the form [x1, x2, ...]; and enter your...
Stoke's theorem says: I (3 x 2). a3 = fh.at Verify Stoke's theorem for the vector field | A = zza +Tgây + yzam and the closed path comprising the straight lines from (0,0,0) to (0,1,0), from (0,1,0) to (0,1,1) and from (0,1,1) to (0,0,0) Hint: The limits of the surface integral are 0 <y < 1 and 0 <zsy.
1 1 -2 Given the LTI system -Ax Bu where A3 3 2and B0 a) Check the controllability using i) the controllability matrix, and ii) the Hautus-Rosenbrock test. b) Identify the controllable and uncontrollable subspaces, and convert the system to a Kalman con- 0 trollable canonical form c) Suppose that we start from the initial state z(0) (1,1, 1)T. Is there a control u(t) that drives the state to (1(3,-1,1)7 at some time t? Is there a control u(t) that...
Problem 3 (20 points) Calculate the 2x2 DCT of the following 2-D signal x[n,n,]=1 L'z 01 et en moderne dhe nuket 2.3.4. sepertirely where ai, ai, a3, and as are the numbers: 2, 3, 4, 5, respectively. (Show your steps)