| Line 8: | Line 8: | ||
\end{bmatrix}=\begin{bmatrix} | \end{bmatrix}=\begin{bmatrix} | ||
-1 &-\frac{1}{2}\\ | -1 &-\frac{1}{2}\\ | ||
| − | frac{1}{2} & -1 | + | \frac{1}{2} & -1 |
\end{bmatrix}\begin{bmatrix} | \end{bmatrix}\begin{bmatrix} | ||
x_1(t) \\ | x_1(t) \\ | ||
x_2(t) | x_2(t) | ||
\end{bmatrix}+\begin{bmatrix} | \end{bmatrix}+\begin{bmatrix} | ||
| − | frac{x_0(t)}{2}\\ | + | \frac{x_0(t)}{2}\\ |
| − | frac{x_3(t)}{2} | + | \frac{x_3(t)}{2} |
\end{bmatrix}=\begin{bmatrix} | \end{bmatrix}=\begin{bmatrix} | ||
-1 &-\frac{1}{2}\\ | -1 &-\frac{1}{2}\\ | ||
| − | frac{1}{2} & -1 | + | \frac{1}{2} & -1 |
\end{bmatrix}\begin{bmatrix} | \end{bmatrix}\begin{bmatrix} | ||
x_1(t) \\ | x_1(t) \\ | ||
x_2(t) | x_2(t) | ||
\end{bmatrix}+begin{bmatrix} | \end{bmatrix}+begin{bmatrix} | ||
| − | frac{1}{2}&0 \\ | + | \frac{1}{2}&0 \\ |
| − | 0& frac{1}{2} | + | 0& \frac{1}{2} |
\end{bmatrix}\begin{bmatrix} | \end{bmatrix}\begin{bmatrix} | ||
x_0(t) \\ | x_0(t) \\ | ||
| Line 31: | Line 31: | ||
ii) | ii) | ||
<math>A=\begin{bmatrix} | <math>A=\begin{bmatrix} | ||
| − | -1 & frac{1}{2} \\ | + | -1 & \frac{1}{2} \\ |
| − | frac{1}{2} & -1 | + | \frac{1}{2} & -1 |
\end{bmatrix}</math> | \end{bmatrix}</math> | ||
Revision as of 01:31, 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} $
