| Line 33: | Line 33: | ||
-1 & \frac{1}{2} \\ | -1 & \frac{1}{2} \\ | ||
\frac{1}{2} & -1 | \frac{1}{2} & -1 | ||
| − | \end{bmatrix}</math> | + | \end{bmatrix}=\begin{bmatrix} |
| + | -1 & 0 \\ | ||
| + | 0 & -1 | ||
| + | \end{bmatrix}+\begin{bmatrix} | ||
| + | 0 & \frac{1}{2} \\ | ||
| + | \frac{1}{2} & 0 | ||
| + | \end{bmatrix}=\begin{bmatrix} | ||
| + | -1 & 0 \\ | ||
| + | 0 & -1 | ||
| + | \end{bmatrix}+\begin{bmatrix} | ||
| + | 1 & 1 \\ | ||
| + | -1 & 1 | ||
| + | \end{bmatrix}\begin{bmatrix} | ||
| + | -\frac{1}{2} & 0 \\ | ||
| + | 0 & \frac{1}{2} | ||
| + | \end{bmatrix}\begin{bmatrix} | ||
| + | \frac{1}{2} & -\frac{1}{2} \\ | ||
| + | \frac{1}{2} & \frac{1}{2} </math> | ||
Revision as of 01:43, 21 May 2017
AC-2 2014
P1. （a）i） $ \begin{bmatrix} x_1(t)\\ x_2(t) \end{bmatrix}=\begin{bmatrix} -1 &-\frac{1}{2}\\ \frac{1}{2} & -1 \end{bmatrix}\begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix}+\begin{bmatrix} \frac{x_0(t)}{2}\\ \frac{x_3(t)}{2} \end{bmatrix}=\begin{bmatrix} -1 &-\frac{1}{2}\\ \frac{1}{2} & -1 \end{bmatrix}\begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix}+begin{bmatrix} \frac{1}{2}&0 \\ 0& \frac{1}{2} \end{bmatrix}\begin{bmatrix} x_0(t) \\ x_3(t) \end{bmatrix} $
ii) $ A=\begin{bmatrix} -1 & \frac{1}{2} \\ \frac{1}{2} & -1 \end{bmatrix}=\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}+\begin{bmatrix} 0 & \frac{1}{2} \\ \frac{1}{2} & 0 \end{bmatrix}=\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix}+\begin{bmatrix} 1 & 1 \\ -1 & 1 \end{bmatrix}\begin{bmatrix} -\frac{1}{2} & 0 \\ 0 & \frac{1}{2} \end{bmatrix}\begin{bmatrix} \frac{1}{2} & -\frac{1}{2} \\ \frac{1}{2} & \frac{1}{2} $
