If the eigenvalue that corresponds to the1eigenvectorfor the matrix4iCc = (-161\is λ = 4i, then which of0the following is a fundamental solution to thesystemX' = CX?4tsin(t)et(14 cos(t)sin(4t)4 cos(4t)cos(4t)-4 sin(4t○ 4 cos(4t)sin(4t)None of the above

To solve this problem, we need to determine the fundamental solution to the system X′=CX given the…

Answered: If the eigenvalue that corresponds to…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Apply the eigenvalue method to find a general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system. x₁ = 2x₁ + 3x2 x'2 = 3x₁ + 2x2 *** The eigenvalue(s) of the constant coefficient matrix is (are) (Use a comma to separate answers as needed. Simplify your answer. Type an exact answer, using radicals and i as needed.)
A 3×3 real matrix has three eigenvalues. One of them is λ₁ = Another is A₂ = 1 + i with eigenvector v2 - (3) = -1 with eigenvector v₁ = (a) What is the third eigenvalue and its corresponding eigenvector? (b) Find the general solution to x' = Ax, in purely real form. (c) Find the solution to x' = Ax subject to initial condition x (0) = (:). (6) 1
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lloa [Ur ses SEC::116 Question 9 Find the general solution to the system x' = Ax where A is the given matrix. -2 -1 1 A= -1 -9 3 -1 -2 -4 Hint: -6 is an eigenvalue.
Suppose that a 2 x 2 matrix A with real entries has an eigenvalue X = 1 + 3i with corresponding 4 i [12] eigenvector 1 + 2i Which of the following is NOT a solution of the linear system y' = Ay? y(t) = et y(t) = et y(t) = et y(t) = et 4 cos(3t) sin(3t) [cos(3t) + 2 sin(3t). 4 cos(3t) + sin(3t) cos(3t) 2 sin (3t) - cos(3t) + 4 sin(3t) 2 cos(3t) + sin(3t) cos (3t) - 4 sin (3t) -2 cos(3t) - sin(3t)
please type in your hand clearly thank you.
Let the matrix M be given by sin o CoS O - sin o M = COS O (i) Is the matrix M invertible? (ii) Calculate M-1 if possible.

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If the eigenvalue that corresponds to the 1 eigenvector for the matrix 4i C c = (-16 1 \ is λ = 4i, then which of 0 the following is a fundamental solution to the system X' = CX? 4t sin(t) et (1 4 cos(t) sin(4t) 4 cos(4t) cos(4t) -4 sin(4t ○ 4 cos(4t) sin(4t) None of the above