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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- 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 yConsider 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) = + C₂9. Using eigenvalues, find the general solution to the following system of equations. x' = -6x + 4y y' = -3x + yFor the linear system y' = 3 Find the eigenvalues and eigenvectors for the coefficient matrix. A1 = , and A2 = v2 =
- Solve the system of differential equations. Find the lesser and greater of the two eigenvalues.For the system of differential equations, X1, X2 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. U₁ = U2 = = y' = 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 A2. 5 2 - 1 Y2 (t) d) Determine two linearly independent solutions to the system. Enter the first solution in the format y₁ (t) y = = y₁ (t) Enter the second solution in the format y₂(t) = ƒ2(t) (v3h₁(t) + v₁h₂(t)) = : fi(t) (vigi(t) – v2g2(t)) . +Help please
- 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 paperCan someone please help with my revision.