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. $\displaystyle \begin{array}{rcl} y_1^{\,\prime} & = & -y_1 \\ y_2^{\,\prime} & = & 2y_1 - y_2 \end{array}$

2. $\displaystyle \boldsymbol{\vec{y}^{\,\prime}} = \left\lbrack \begin{array}{rr} 2 & 0 \\ 0 & 2 \end{array} \right\rbrack \boldsymbol{\vec{y}}$

3. $\displaystyle \begin{array}{rcl} y_1^{\,\prime} & = & y_1 + y_2 \\ y_2^{\,\prime} & = & y_2 \end{array}$

4. $\displaystyle \boldsymbol{\vec{y}^{\,\prime}} = \frac{1}{2} \left\lbrack \begin{array}{rr} -0.5 & 0 \\ 0 & -0.5 \end{array} \right\rbrack \boldsymbol{\vec{y}}$



A		B



C		D

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