The state variable representation of a system is given as

x˙=[0101]x;x(0)=[10]y=[01]x

The response y(t) is

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  1. sin t
  2. 1 - et
  3. 1 - cos t
  4. 0

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Option 4 : 0
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X˙=AX, where A=[0101] is state transition matrix.

Thus, we have

X(s)=(sIA)1X(0)X(s)=[s10s+1]1[10]X(s)=1s(s+1)[s+110s][10]X(s)=1s(s+1)[s+10]X(s)=[1s0]x(t)=[10]

Now, 

y(t)=[01]x=[01][10]=0

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