An unforced linear time-invariant (LTI) system is represented by: \left[\begin{array}{c}˙{x\end{array}_1 ; ˙{x}_2]}=\left[\begin{array}{cc}-1 & 0 \ 0 & -2]\end{array}\left[\begin{array}{c}x_1 \ x_2]\end{array} If the initial condition are x 1 (0) = 1 and x 2 (0) = -1, the solution of the state equation is

Correct Answer is : x1(t) = e-t, x2(t) = -e-2t

x 1 (t) = -e -t , x 2 (t) = 2e -t

x 1 (t) = e -t , x 2 (t) = -e -2t

x 1 (t) = -e -t , x 2 (t) = -2e -t

GATE Electronics and Communications (EC) 2014 Shift 2 Solved Paper

Question : 56 of 65

Marks: +1, -0

An unforced linear time-invariant (LTI) system is represented by:

{[\table ˙{x}_1 ; ˙{x}_2]}={[\table -1 , 0 ; 0 , -2]}{[\table x_1 ; x_2]}

If the initial condition are x₁(0) = 1 and x₂(0) = -1, the solution of the state equation is

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