WeBWorK Standalone Renderer

Match each linear system with one of the phase plane direction fields.
(The blue lines are the arrow shafts, and the black dots are the arrow tips.)

1. $\displaystyle \boldsymbol{\vec{x}^{\,\prime}} = \left\lbrack \begin{array}{rr} -2 & -10 \\ 1 & -4 \end{array} \right\rbrack \boldsymbol{\vec{x}}$

2. $\displaystyle \boldsymbol{\vec{x}^{\,\prime}} = \left\lbrack \begin{array}{rr} -3 & 1 \\ 3 & -1 \end{array} \right\rbrack \boldsymbol{\vec{x}}$

3. $\displaystyle \boldsymbol{\vec{x}^{\,\prime}} = \left\lbrack \begin{array}{rr} 6 & -9 \\ 2 & 0 \end{array} \right\rbrack \boldsymbol{\vec{x}}$

4. $\displaystyle \boldsymbol{\vec{x}^{\,\prime}} = \left\lbrack \begin{array}{rr} 9 & -3 \\ -1 & 7 \end{array} \right\rbrack \boldsymbol{\vec{x}}$



A		B



C		D

Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are real or complex and positive or negative.

In order to get credit for this problem all answers must be correct.