(1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix....
(1 point) Consider the linear system "(-1: 1) y. a. Find the eigenvalues and eigenvectors for the coefficient matrix. 1 v1 = and 2 V2 b. For each eigenpair in the previous part, form a solution of y' = Ay. Use t as the independent variable in your answers. (t) = and yz(t) c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Choose
Consider the linear system y⃗ ′=[6−124−8]y⃗ . Problem 1. (10 points) Consider the linear system 4 ' = [-12 -8 a. Find the eigenvalues and eigenvectors for the coefficient matrix. te and 12 = v2 = b. For each eigenpair in the previous part, form a solution of y' = Ay. Use t as the independent variable in your answers. gi(t) = and yz(t) = c. Does the set of solutions you found form a fundamental set (i.e., linearly independent...
please include each and every step and solve all the parts Previous Problem Probl em List Next Problem (1 point) Consider the linear system 6 -41 12 8 a. Find the eigenvalues and eigenvectors for the coefficient matrix and λ2- V1- 02 b. For each eigenpair in the previous part, form a solution of y,-ay Use t as the independent variable in your answers. and y2 (t)-- i(t) c. Does the set of solutions you found form a fundamental set...
(1 point) Consider the linear system 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix 0 and A b. Find the real valued solution to the initial value problem -392 5y + 3y (0) 9, y(0) - -10. Use t as the independent variable in your answers, (t)
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. 1 = . and 12 = V2 = b. Find the real-valued solution to the initial value problem = -3y - 2y, 5y + 3y2 (0) = -11, y (0) = 15. Usef as the independent variable in your answers. y (t) = (1) =
(1 point) Consider the linear system -3 -2 333 5 a. Find the eigenvalues and eigenvectors for the coefficient matrix. di = and 12 02 b. Find the real-valued solution to the initial value problem syi ly -341 – 2y2, 5y1 + 3y2, yı(0) = 11, y2(0) = -15. Use t as the independent variable in your answers. yı(t) y2(t)
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. and iz = b. Find the real-valued solution to the initial value problem - -3y - 2y2 Syı + 3y2 yı(0) = -7, (0) = 10 Use I as the independent variable in your answers. Y() = Note: You can earn partial credit on this problem. Problem 6. (1 point) Find the most general real-valued solution to the linear system of differential...
(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) Consider the linear system -3 -2 - 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 2 and 2 =i -3+i -3-i b. Find the real-valued solution to the initial value problem — Зул — 2у2, y1 (0)=-6, โบ,่ y2(0)= 15 5уд + Зуз, Use t as the independent variable in your answers. y1 (t) -6cos(t)+5sin(t) У2(t) 15cost+15sint
(1 point) Consider the linear system 3 y y 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 0 and A2 = -1 02 -3- -3+1 b. Find the real-valued solution to the initial value problem Svi C = -3y - 2y2, 591 +372 y.(0) = 6, 32(0) = -15. Use t as the independent variable in your answers. yı() y2(t) = 0