For the system of differential equations,323 846 - 224eta) Find the characteristic polynomial of the matrix of coefficients A.CA(X)A1, A2b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending orderseparated by commas.U₁ =U₂ =c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smallereigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue λ₂. Enterthe eigenvectors as a matrix with an appropriate size.y'=v(t)y +d) Determine a general solution to the system by completing the following steps.i. Find v(t) = [Y-¹(t)f(t)dt .ii. Find a particular solution y(t).Hyp(t)=y(t)ii. Then a general solution for the system in the matrix form is-8:33:

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or the system of differential equations, y² = [ 28 23 84 -6 - 22 O Find the characteristic polynomial of the matrix of coefficients A. CA(X): A1, A2 = ) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order eparated by commas. 21 3 4et y + Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller igenvalue A₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter ne eigenvectors as a matrix with an appropriate size. = U₂ =