Question

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 $<u,v>.$

          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 $<u,v>.$

Consider the differential equation for the vector-valued function x,
x' = Ax, A =
< b m a t r i x >
Find the eigenvalues λ1, λ2 and their corresponding eigenvectors v1, v2 of the coefficient matrix A.
(a) Eigenvalues:
λ1, λ2 = 2+3i, 2-3i
Note: You must enter two numbers separated by a comma.
(b) Eigenvector for λ1 you entered above:
v1 = <-3i, 1>
(c) Eigenvector for λ2 you entered above:
v2 = <3i, 1>
(d) Use the eigenpairs you found in parts (a)-(c) to find real-valued fundamental solutions to the differential equation above.
x1 =
x2 =
Note: To enter the vector (u, v) type <u,v>.

Added by Elizabeth M.

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