Question

a. Find the eigenvalues and eigenvectors of the matrix $\begin{bmatrix} -1 & -6\\ 0 & -7 \end{bmatrix}$. $\lambda_1 = -7$, $v_1 = \begin{bmatrix} 1\\ 1 \end{bmatrix}$, and $\lambda_2 = -1$, $v_2 = \begin{bmatrix} 1\\ 0 \end{bmatrix}$ b. Solve the system of differential equations $Y' = \begin{bmatrix} -1 & -6\\ 0 & -7 \end{bmatrix} Y$ satisfying the initial conditions $\begin{bmatrix} y_1(0)\\ y_2(0) \end{bmatrix} = \begin{bmatrix} 1\\ -1 \end{bmatrix}$. $y_1(t) = $ y_2(t) =

          a. Find the eigenvalues and eigenvectors of the matrix $\begin{bmatrix} -1 & -6\\ 0 & -7 \end{bmatrix}$.
$\lambda_1 = -7$, $v_1 = \begin{bmatrix} 1\\ 1 \end{bmatrix}$, and $\lambda_2 = -1$, $v_2 = \begin{bmatrix} 1\\ 0 \end{bmatrix}$
b. Solve the system of differential equations $Y' = \begin{bmatrix} -1 & -6\\ 0 & -7 \end{bmatrix} Y$
satisfying the initial conditions $\begin{bmatrix} y_1(0)\\ y_2(0) \end{bmatrix} = \begin{bmatrix} 1\\ -1 \end{bmatrix}$.
$y_1(t) = 
$
y_2(t) =

a. Find the eigenvalues and eigenvectors of the matrix < b m a t r i x >.
λ1 = -7, v1 =
< b m a t r i x >, and λ2 = -1, v2 =
< b m a t r i x >
b. Solve the system of differential equations Y' =
< b m a t r i x >
Y
satisfying the initial conditions < b m a t r i x >
=
< b m a t r i x >.
y1(t) =
y2(t) =

Added by Hannah P.

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