4. Problem 4. Consider the following system of first order coupled ordinary differential equation...
Problem 13.13. Consider the system of three linear differential equations: xt = 2x1 + 3x2 + 4.13 where the unknowns are the three functions xi(t), x2(t), and 23(t). x'a = 2x2 + 6.13 (a) Write the system in the form x' = Ax, where A is a (3 x 3) matrix. X'z = 2x3 (b) Write A as the sum of two matrices, A=D+U, where D is a diagonal matrix (all of the off-diagonal entries are zero, and the diagonal...
Problem #2: Consider the following vectors, which you can copy and paste directly into Matlab. x=[3 4 4 3 5 5 1 2 32); y [2 4 4622 4 2 4] Use the vectors x and y to create the following matrix. 3 2 0 0 0 0 0 0 0 o Such a matrix is called a tri-diagonal matrix. Hint: Use the diag command three times, and then add the resulting matrices. To check that you have correctly created...
2. [-12 Points) DETAILS LARLINALG8 7.2.005. Consider the following. -4 20 0 1 -3 A = 040 P= 04 0 4 0 2 1 2 2 (a) Verify that A is diagonalizable by computing p-AP. p-1AP = 11 (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. (91, 12, 13)...
Publish using a MatLab function for the following: If a matrix A has dimension n×n and has n linearly independent eigenvectors, it is diagonalizable.This means there exists a matrix P such that P^(−1)AP=D, where D is a diagonal matrix whose diagonal entries are made up of the eigenvalues of A. P is constructed by taking the eigenvectors of A and using them as the columns of P. Your task is to write a program (function) that does the following If...
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
Consider the system of two coupled differential equations: y-cx + dy, x-ax + by, with the equilibrium solution (xe,ye) = (0,0) (a) Rewrite the coupled system as a matrix differential equation and identify the matrix A. Obtain a general solution to the matrix differential equation in terms of eigenvectors and eigenvalues of A. Justify your answer (b) Classify possible types and stability of the equilibrium with dependence on the eigenvalues of A. (Note: You are not asked to compute the...
Linear Algebra system of differential equation and symmetric matrices please elaborate every step so that it gets easier to understand thank you 6.3-Systems of Diff Eq: Problem 1 Previous Problem Problem List Next Problem (1 point) Let (t) = be a solution to the system of differential equations: 22(t) (t) x'(t) = = 331(t) + 2x2(t) -11(t) If x(0) = , find r(t) Put the eigenvalues in ascending order when you enter 2(t), 22(t) below. 31(t) = expl t)+ exp...
Consider the following linear system of differential equations: dx/dt = 2x-3y dy/dt = -x +4y (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given x(0) = 3 and y(0) = 4 (d) Verify the calculations with MATLAB
I need help with Q12) please and eigenvectors of the row-echelon matrix VWV) 37dldl IV 31076 IW NO LOHS 1 U = 2 -4 0 2 1 0 0 3 0 0 0 3 --3 3 5 d the eigenvalues and eigenvectors of the following matrices. a) A= 1 3 0 2 2 0 0 0 6 3 0 b) B= 0 -4 0 6 0 -1 3 Problems 8.2 : Eigenvectors, bases, and diagonalisation 11. [R] For each of...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).