We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
($ ?) 4 2. (a) Find the eigenvalues and eigenvectors of the matrix 3 Hence or...
a) Find the eigenvalues and the eigenvectors of the 2x2 matrix: [4 2] [3 -1] b) Solve the initial value problem: dx/dt = 4x + 2y dy/dt = 3x - y with x(0) = 0, y(0) = 7
Find the eigenvalues and eigenvectors of the matrix A - = -3 10 2 —4
Consider the 3 x 3 matrix A-1-ovvT where a R, 1 is the identity matrix and v the vector (a) Determine the eigenvalues and eigenvectors of A (b) Hence find a matrix which diagonalises A. (c) For which a is the matrix A singular? (d) For which α is the matrix A orthogonal ? Consider the 3 x 3 matrix A-1-ovvT where a R, 1 is the identity matrix and v the vector (a) Determine the eigenvalues and eigenvectors of...
2. Find eigenvalues and eigenvectors of the matrix and check if they are linearly independent A - 12 11 Ō SETY (30 marks)
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
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) = {.
(a) Find the eigenvalues of the matrix 4) 2 1' and find an eigenvector corresponding to each eigenvalue. Hence find an invertible matrix, P, and a diagonal matrix, D, such that P-1AP = D. (b) Use your result from (a) to find the functions f(t) and g(t) such that f(t)-f(t) +2g(t) g(t) 2f(t) g(t), where f(0)-1 and g(0)-2 (c) Now suppose that f(0)-α and g(0) β. Determine the condition(s) on α and β that must hold if, as t,t is...
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-
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!<