Consider the differential equation for the vector-valued function x,
\(x' = Ax,\quad A = \begin{bmatrix} 2 & 9 \\ -1 & 2 \end{bmatrix}\)
Find the eigenvalues $\lambda_1, \lambda_2$ and their corresponding eigenvectors $v_1, v_2$ of the coefficient matrix A.
(a) Eigenvalues:
$\lambda_1, \lambda_2 = 2+3i, 2-3i$
Note: You must enter two numbers separated by a comma.
(b) Eigenvector for $\lambda_1$ you entered above:
$v_1 = <-3i, 1>$
(c) Eigenvector for $\lambda_2$ you entered above:
$v_2 = <3i, 1>$
(d) Use the eigenpairs you found in parts (a)-(c) to find real-valued fundamental solutions to the differential equation above.
$x_1 = $
$x_2 = $
Note: To enter the vector $(u, v)$ type $<u,v>.$
