Solve the initial value problem given below. In your solving process, make sure to (1) write the system in matrix form; (2) find eigenvalues; (3) find eigenvectors; (4) use initial conditions to find c1 and c2, and (5) state your solution. You may work this out by hand or using MATLAB, but are strongly encouraged to do both as a check on your work. dx dt dy dt = x + 3y, = : 3x + y, x (0) = 3 y (0) = 1

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Kindly solve this question on matrix, refer to the screenshot;

Linear algebra: please correctly and handwritten

1 4 2 4 Find the eigenvalues of the following matrix : C= 2 2

Consider the given matrix. Find the eigenvalues. (Enter your answers as a comma-separated list.) λ = 1.2.3 3 0 0 2 0 4 0 1 Find the eigenvectors. (Enter your answers in order of the corresponding eigenvalues, from smallest eigenvalue to largest.) X K1 = 1 0 -2 Need Help? Read It

Please help with questions 2 and 3.