Find the fundamental matrix for the two-dimensional system defined by * = x, + txz, *2...
Let X be a 4-dimensional random vector defined as X = [X1 correlation matrix X4' with expected value vector and X2 X3 E[X] =| | , 1 1 -1 0 Rx-10-11-1 0 0 0-1 1 Let Y be a 3-dimensional random vector with (a) Find a matrix A such that Y -AX. (b) Find the correlation matrix of Y, that is Ry (c) Find the correlation matrix between X1 and Y, that is Rx,Y
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 4 = 2 with vi = and |_ G 12 = -2 with v2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: x(t) (50) = C1 + C2 e e B. In fundamental matrix form: (MCO) = I: C. As two equations: (write "c1" and "c2" for C1 and c2) x(t) = yt) =
Consider the 3-dimensional system of linear equations 1 1 1 X' = X 2 1 -1 0-1 1 (a) Find a fundamental set of solutions for this system. Note that -1 is one of the eigenvalues (b) Find the general solution, and use it to find the solution satisfying -4 X(0) 2 Consider the 3-dimensional system of linear equations 1 1 1 X' = X 2 1 -1 0-1 1 (a) Find a fundamental set of solutions for this system....
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to the linear system AF in the following forms A. In eigenvalueleigenvector form r(t) B. In fundamental matrix form z(t) v(t) C. As two equations: (write "c1* and "c2" for ci and C2) a(t)- v(t)- (1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to the linear system AF in the...
(1 point) In this problem you will solve the nonhomogeneous system 1 A. Write a fundamental matrix for the associated homogeneous system = B. Compute the inverse C. Multiply by g and integrate +ci dt +c2 (Do not include c and c2 in your answers). D. Give the solution to the system C1+ (Do not include ci and c2 in your answers). If you don't get this in 2 tries, you can get a hint. (1 point) In this problem...
(1 point) In this problem you will solve the nonhomogeneous system -3 5]- -5 3 y t A. Write a fundamental matrix for the associated homogeneous system B. Compute the inverse C. Multiply by g and integrate tci (Do not include c1 and c2 in your answers). D. Give the solution to the systenm C + (Do not include ci and c2 in your answers). (1 point) In this problem you will solve the nonhomogeneous system -3 5]- -5 3...
Suppose that the matrix A A has the following eigenvalues and eigenvectors: (1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0...
Find a fundamental matrix of the system y'=Ay for A = 012 2
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
Using matrix algebra, find a general solution to the following system of equations x' = 3x - 4y and y' = 4x - 7yUsing matrix algebra, find a general solution to the following system of equations: x' = 3x - 4y y' = 4x - 7y The general solution functions are: ( use c1 and c2 as the constants and enter the elements of the eigenvectors as the lowest integer values. If one element of an eigenvector has a negative value enter the first element...