Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix (3 2 6 1...
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 4. (20 pts.) a) In the following system of linear equations, find k such that the system Has unique solution Has infinitely many solutions Has no solution x+z=0 x + 2y + 2z = 3 (x + kk + 1)y + z = k Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 13 2 6 1 -2 3 16 4 12 b) Find the Fourier series representation of the function with period 21 given by...
12) (20 pts total) Find the eigenvalues and eigenvectors of the following matrix, Choose x1=1: [2/4 0 -1; 01/26; 1/204) (20 pts)Find the inverse of the matrix from question 12. I te To keep up-to-date with security updates, fixes, and improvements, choose Check for Upd c (2-1) 12) (20 pts total) Find the eigenvalues and eigenvectors of the following matrix, Choose x1=1: [2/40-1; 01/26;1/204) (20 pts) Find the inverse of the matrix from question 12.
($ ?) 4 2. (a) Find the eigenvalues and eigenvectors of the matrix 3 Hence or otherwise find the general solution of the system = 4x + 2y = 3x - y 195 marks 5. (a) Give a precise definition of Laplace transform of a function f(t). Use your definition to determine the Laplace transform of 3. Osts 2 6-t, 2 <t f(t) = [20 marks] (b) A logistic initial value problem is given by dP dt kP(M-P), P(0) -...
12) (20 pts total) Find the eigenvalues and eigenvectors of the following matrix, Choose x1=1: [ 2/4 0 -1; 01/26; 1/204]
Find the eigenvalues and eigenvectors of the matrix 6 5 B- [ -5-2
Find the matrix A that has the given eigenvalues and corresponding eigenvectors. Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A= Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A=
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6 -12 A-3 -16, (3 3 8 and also find an invertible matrix P and a diagonal matrix D such that D=P-AP or A = PDP-
8. 20 pts.] Suppose that a 2 x2 matrix A has the following eigenvalues and eigenvectors: () 12, 1 r2=1, 2 2 (a) Classify the equilibrium 0 (node, saddle, spiral, center). Is it stable or unstable? (b) Sketch the trajectories of the system A , where a the phase plane below. (c) On the next page, sketch the graphs of r1 (t) and 2(t) versus t for the solution that satisfies the initial condition x1(0) = 1, x2(0) = 1...
3. Find all eigenvalues and eigenvectors of the matrix -20 2 -1 0 2 0-2 1