(a) We have, the eigenvectors of the coefficient matrix are given by the roots of the characteristic equation, so
Thus, the eigenvalues of the coefficient matrix are
An eigenvector corresponding to the eigenvalue i is given by
and, an eigenvector corresponding to the eigenvalue -i is
So, the answer to (a) is
(b) Now, we have
Now, in our case
and
So, the general solution of the given system is
Simplifying we get
Now, we have the initial condition,
Applying this initial condition we get
so our particular solution is
Simplifying further we have
Thus, writing down the functions separately, the solution to (b) is
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the...
(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. 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 ' = y. -5 -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 = 15 and 2 V2 b. Find the real-valued solution to the initial value problem Syi ly 3y1 + 2y2, -541 – 3y2, yı(0) = 0, y2(0) = -5. Use t as the independent variable in your answers. yı(t) y2(t)
(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
(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)
Previous Problem Problem List Next Problem (1 point) Consider the linear system -3 -2 >= -3) y. 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. di = on = and 12 = · U2 b. Find the real-valued solution to the initial value problem { vi = -3yı – 2y2, 5yı + 3y2, yı(0) = 11, y2(0) = -15. y۔ = Use t as the independent variable in your answers. yı(t) = y2(t) =
Please answer all parts and box answers (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. b. Find the real-valued solution to the initial value problem S = = 3y + 2y, -5yı - 3y2 10) = 1, 20) = -5. Usef as the independent variable in your answers. y (4) = y =
PLEASE ANSWER AND FILL IN ALL ANSWER BOXES PLEASE ANSWER ALL QUESTIONS ASKED (1 point) Consider the linear system ;' = -5 -3): a. Find the eigenvalues and eigenvectors for the coefficient matrix. 21 = v= and 12 = V2= II b. Find the real-valued solution to the initial value problem 3yı + 2y2, y = -5yı - 3y2, yı(0) = -4, y2(0) = 10. Use t as the independent variable in your answers. yı(t) = y2(t) =
1 of the questions remains unanswered. (1 point) Consider the linear system -3-1 a. Find the eigenvalues and eigenvectors for the coefficient matrix -3+1 AI 01 5 and Az 02 5 b. Find the real-valued solution to the initial value problem { - 3y - 2 5y1 +32 (0) - 10, (0) --15. Use as the independent variable in your answers. m (0) (0) Note: You can earn partial credit on this problem Preview My Answers Submit Answers Your score...
(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