Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right).$$
If the initial state vector of the system is $$x\left( 0 \right) = \left[ {\matrix{ 1 \cr { - 2} \cr } } \right],$$
then the system response is $$x\left( t \right) = \left[ {\matrix{ {{e^{ - 2t}}} \cr { - 2{e^{ - 2t}}} \cr } } \right].$$
If the initial state vector of the system changes to $$x\left( 0 \right) = \left[ {\matrix{ 1 \cr { - 1} \cr } } \right],$$
then the system response becomes $$x\left( t \right) = \left[ {\matrix{ {{e^{ - t}}} \cr { - {e^{ - t}}} \cr } } \right].$$

The system matrix a is

X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s complement format. The sum of X and Y represented in two’s complement format using 6 bits is:

In the digital-to-Analog converter circuit shown in the figure below,
$${V_{R\,}}\, = \,10V$$ and $$R\, = \,10k\Omega $$

The voltage V₀ is

In the digital-to-Analog converter circuit shown in the figure below,
$${V_{R\,}}\, = \,10V$$ and $$R\, = \,10k\Omega $$

The current i is