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QUESTION 18 The 2 x 2 matrix A= has complex eigenvalues r = -2£i. An eigenvector...
QUESTION 18 The 2 x 2 matrix A= has complex eigenvalues r = -2£i. An eigenvector corresponding 2 to r = -2+ i is 1-) The system x' = Ax+ (). e-2t has one solution given by x(t) = (2) e-2t. What is the general solution to the system? C1 cost sint - cost 6) -27 +02 e sint sint - cost :) -21 e + (1) e OB C1 cost cost 0-2t + C2 0 sint e-2t + (1)...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 4 = 2...
(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) =
Suppose that the matrix A A has the following eigenvalues and eigenvectors: (1 point) Suppose that...
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: A1 = 4...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: A1 = 4 with = and [2] [i] Az = 3 with Ū2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t (10) -- + C2 e e B. In fundamental matrix form: (39) - g(t). C. As two equations: (write "c1" and "c2" for C and C2) X(t) = g(t) = Note: if you are...
If one eigenvalue of a 2 by 2 matrix E2x2 is 1 = 7 and a...
If one eigenvalue of a 2 by 2 matrix E2x2 is 1 = 7 and a corresponding eigenvector of is ( 2) , then the general solution of the system ODES: = (t) = E2x2 f(t) cost sint is ä(t) = C: + C2 sin cost can't be determined. Solving the system requires additional information sint COS is 8(t) + C2 pot cost sint cost sint is i(t) = C: + C2 sint COS
Determine e At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula eAt = X(t)X(0)1. 0...
Determine e At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula eAt = X(t)X(0)1. 0 2 2 2 0 2 2 2 0 First, find X(t). Choose the correct answer below 4t -2t 4t e -2t (1+t) e e -2t OA. X(t) (1+t)e4t 0 e2t B. X(t)= e4t 0 -2t -2t 2t - e - 2t (1t)e 4t e e 4t e 4t - sint sin t 0 (1t)e -2t O C....
24. Let A be a 2 x 2 real constant coefficient matrix. Suppose the system of...
24. Let A be a 2 x 2 real constant coefficient matrix. Suppose the system of differential equations x(t) = Ax(t) has a fundamental matrix X(t) = parameters is used to find a particular solution of the form . When the method of variation of e e2t Xp(t) = X(t)1、100 1 tox'(t) which of the following is a correct choice for vi()? A. 2t B. 2 D. 3e-t E. 2e2t
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors 2-2i and -2+2i Write the solution to...
(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...
2 2 X Questions 17 and 18 will deal with the linear system X' = -...
2 2 X Questions 17 and 18 will deal with the linear system X' = - 2 3 pts Question 17 What are the eigenvalues to the linear system? Select the correct answer O 0,-4 O 2,2 O-2 2i 0,4 O 22i 4 pts Question 18 The solution of the linear system is Select the correct answer O None of the above (C X ce2 sin(2t) e cos(2t) 1 cos(2t) 0 sin(2t) 1 25 X c1e -2t sin(t) ce' cost...
The 2 x 2 matrix 1 = ( 43 II has two distinct real eigenvalues. 1....
The 2 x 2 matrix 1 = ( 43 II has two distinct real eigenvalues. 1. Give the characteristic polynomial for A in Maple notation in the form t^2 + a*t + b Characteristic polynomial = 2. Find the set of eigenvalues for A, enclosed in braces , ) with the two eigenvalues separated by a comma, like (-4, 7) Set of eigenvalues for A = 5 3. Find one eigenvector for each eigenvalue, using Maple > for vectors, e.g....
QUESTION 18 The 2 x 2 matrix A= has complex eigenvalues r = -2£i. An eigenvector corresponding 2 to r = -2+ i is 1-) The system x' = Ax+ (). e-2t has one solution given by x(t) = (2) e-2t. What is the general solution to the system? C1 cost sint - cost 6) -27 +02 e sint sint - cost :) -21 e + (1) e OB C1 cost cost 0-2t + C2 0 sint e-2t + (1)...
(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) =
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: A1 = 4 with = and [2] [i] Az = 3 with Ū2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t (10) -- + C2 e e B. In fundamental matrix form: (39) - g(t). C. As two equations: (write "c1" and "c2" for C and C2) X(t) = g(t) = Note: if you are...
If one eigenvalue of a 2 by 2 matrix E2x2 is 1 = 7 and a corresponding eigenvector of is ( 2) , then the general solution of the system ODES: = (t) = E2x2 f(t) cost sint is ä(t) = C: + C2 sin cost can't be determined. Solving the system requires additional information sint COS is 8(t) + C2 pot cost sint cost sint is i(t) = C: + C2 sint COS
Determine e At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula eAt = X(t)X(0)1. 0 2 2 2 0 2 2 2 0 First, find X(t). Choose the correct answer below 4t -2t 4t e -2t (1+t) e e -2t OA. X(t) (1+t)e4t 0 e2t B. X(t)= e4t 0 -2t -2t 2t - e - 2t (1t)e 4t e e 4t e 4t - sint sin t 0 (1t)e -2t O C....
24. Let A be a 2 x 2 real constant coefficient matrix. Suppose the system of differential equations x(t) = Ax(t) has a fundamental matrix X(t) = parameters is used to find a particular solution of the form . When the method of variation of e e2t Xp(t) = X(t)1、100 1 tox'(t) which of the following is a correct choice for vi()? A. 2t B. 2 D. 3e-t E. 2e2t
(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...
2 2 X Questions 17 and 18 will deal with the linear system X' = - 2 3 pts Question 17 What are the eigenvalues to the linear system? Select the correct answer O 0,-4 O 2,2 O-2 2i 0,4 O 22i 4 pts Question 18 The solution of the linear system is Select the correct answer O None of the above (C X ce2 sin(2t) e cos(2t) 1 cos(2t) 0 sin(2t) 1 25 X c1e -2t sin(t) ce' cost...
The 2 x 2 matrix 1 = ( 43 II has two distinct real eigenvalues. 1. Give the characteristic polynomial for A in Maple notation in the form t^2 + a*t + b Characteristic polynomial = 2. Find the set of eigenvalues for A, enclosed in braces , ) with the two eigenvalues separated by a comma, like (-4, 7) Set of eigenvalues for A = 5 3. Find one eigenvector for each eigenvalue, using Maple > for vectors, e.g....
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