The correct option is B [A]=⎡⎢⎣010001−3−5−4⎤⎥⎦;[B]=⎡⎢⎣001⎤⎥⎦
For the given system we can write,
Y(s)[s3+4s2+5s+3]=U(s)[1] ....(i)
Let, x1=y
So, x2=˙x1=˙y ...(ii)
x3=˙x2=¨y ....(iii)
The equation (i) can be written as
˙x3+4x3+5x2+3x1=u
i.e. ˙x3=−3x1−5x2−4x3+u ...(iv)
Using equation (ii), (iii) and (iv) we can write in state variable form as below,
⎡⎢⎣˙x1˙x2˙x3⎤⎥⎦=⎡⎢⎣010001−3−5−4⎤⎥⎦⎡⎢⎣x1x2x3⎤⎥⎦+⎡⎢⎣001⎤⎥⎦u
So [A]=⎡⎢⎣010001−3−5−4⎤⎥⎦
and [B]=⎡⎢⎣001⎤⎥⎦
Hence option (b) is correct.