(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: A1 = 4...
(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) =
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: X= -4 with eigenvector v = and generalized eigenvector ū= [] (-1) Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t t [CO] = C1 + C2 + I g(t). e . - 1 B. In fundamental matrix form: [CO] C. As two equations: (write "c1" and "c2" for 1 and 2) X(t)...
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...
(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) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: i = -3 with eigenvector v = and generalized eigenvector w= = [-] = [4] Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: 1 (O) = - 18.05.8:8)... y(t) B. In fundamental matrix form: (O)- x(1) y(t) [:] C. As two equations: (write "c1" and "c2" for c and c2) X(t) = yt)...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
-21 9 (1 point) Find eigenvalues and eigenvectors for the matrix -54 24 The smaller eigenvalue has an eigenvector The larger eigenvalue has an eigenvector
(1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. , and 12 = -:| b. For each eigenpair in the previous part, form a solution of ý' = Ay. Use t as the independent variable in your answers. ý (t) = and yz(t) = c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Choose
(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 V2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
(1 point) Find the eigenvalues , < 12 <13 and associated unit eigenvectors ul, 2, uz of the symmetric matrix -2 -2 - 2 0 A= 4 -2 -4 0 The eigenvalue 11 -6 has associated unit eigenvector új 1 1 1 The eigenvalue 12 has associated unit eigenvector iz 0 -2 1 1 The eigenvalue 12 0 has associated unit eigenvector üg -2 1 1 The eigenvalue 3 = 4 has associated unit eigenvector ūg 0 -1 1 Note:...