1. For the system of linear differential equations below find the eigenvalues and eigen vectors of the coefficient matrix. Construct the fundamental set of solutions. x' = 6x-3y y² = 2x + y
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- Find the eigenvalues and eigenvectors for the coefficient matrix.λ1 = -2, λ2=5 V1 = (1, -2) V2 = (4, -1) Using the above eigenvalues and/or eigenvectors, find the general solution of the following system of linear differential equations, writing the solution as an equation for x and an equation for y: x ̇= 6x+4yy ̇ = − 2 x − 3 yλ1 = -2, λ2=5 V1 = (1, -2) V2 = (4, -1) Using the above eigenvalues and/or eigenvectors, find the general solution of the following system of linear differential equations, writing the solution as an equation for x and an equation for y: x = 6x+4yy = − 2 x − 3 y
- Q3: Find the eigenvalues and eigenvectors for the following system * = y = 2x+y 3x-2y.Consider the linear system X1 = and Find the eigenvalues and eigenvectors for the coefficient matrix. A₂ = 0 JI ← A, V₁ 9 V2 = 81 = = -3 6 - - 4 x. help (numbers) help (matrices) help (numbers) help (matrices) For each eigenpair in the previous part, form a solution of a' = Ax. Use t as the independent variable in your answers.For the system of differential equations, = A₁, A₂ = U₁ = U2 = y' a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) = [16 b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. = -16 21 C1 c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue X₂ . Enter the eigenvectors as a matrix with an appropriate size. 14 19 y d) Determine a general solution to the system. Enter your answer in the format y(t) = c₁f₁(t)ví + c₂f₂(t)v₂ . y(t) = + C₂
- Solve the system of differential equations. Find the lesser and greater of the two eigenvalues.Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. (-3+i) A₁ = 1 , vi b. Find the real-valued solution to the initial value problem [{ and A₂ = -3y1 - 2/2, 591 +33/2, Use t as the independent variable in your answers. vi(t) =(5-5/2i)e^(-it)(-3/5-1/5)+(5+5/2i)e^(it)(-3/5+i/5) 32(t)= (5-5/2)^(-it)+(5+5/2)^(it) 4 vo = 3/1 (0) = 6, 3/2 (0) = -5. (-3-1)/please solve it on the paper
- The eigenvalue andfind the eigenvector show the complete solutionSuppose a system of constant coefficient differential equations z'- Az has a 2 x 2 matrix A with 1 Find the real part ₁ and the eigenvalues A1, A₂ = 262 and A₁ = 2 + 6¿ has eigenvector -1+ ¿ imaginary part ₂ and write the fundamental matrix [1₂] for the general solution: