1.

Which one of the following systems is completely state controllable?

A. <table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub> </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> = </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td><center>-1</center></td><td></td><td> </td><td><center>0</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> + </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>2</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2">u</td></tr><tr><td>x<sub>2</sub> </td><td><center>0</center></td><td></td><td></td><td><center>-2</center></td><td>x<sub>2</sub></td><td>1</td></tr></table>
B. <table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub> </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> = </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td><center>-1</center></td><td></td><td> </td><td><center>0</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> + </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>2</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2">u</td></tr><tr><td>x<sub>2</sub> </td><td><center>0</center></td><td></td><td></td><td><center>-2</center></td><td>x<sub>2</sub></td><td>0</td></tr></table>
C. <table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub> </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> = </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td><center>1</center></td><td></td><td> </td><td><center>1</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> + </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>1</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2">u</td></tr><tr><td>x<sub>2</sub> </td><td><center>0</center></td><td></td><td></td><td><center>-1</center></td><td>x<sub>2</sub></td><td>0</td></tr></table>
D. <table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub> </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> = </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td><center>0</center></td><td></td><td> </td><td><center>0</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> + </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>2</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2">u</td></tr><tr><td>x<sub>2</sub> </td><td><center>2</center></td><td></td><td></td><td><center>-2</center></td><td>x<sub>2</sub></td><td>2</td></tr></table>
Answer» B. <table><tr><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub> </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> = </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td><center>-1</center></td><td></td><td> </td><td><center>0</center></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>x<sub>1</sub></td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2"> + </td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-obracket-h1.gif"></td><td>2</td><td rowspan="2"><img src="https://www.indiabix.com/_files/images/data-interpretation/common/15-sym-cbracket-h1.gif"></td><td rowspan="2">u</td></tr><tr><td>x<sub>2</sub> </td><td><center>0</center></td><td></td><td></td><td><center>-2</center></td><td>x<sub>2</sub></td><td>0</td></tr></table>


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