GATE IN 2013 Question Paper (10-Feb-2013) (Shift 2)

The dimension of the null space of the matrix $\left[\begin{array}{ccc}0& 1& 1\\ 1& -1& 0\\ -1& 0& -1\end{array}\right]$ is

If the A-matrix of the state space model of a SISO linear time invariant system is rank deficient, the transfer function of the system must have

Two systems with impulse responses h₁(t) and h₂ (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

The complex function tanh (s) is analytic over a region of the imaginary axis of the complex s-plane if the following is TRUE everywhere in the region for all integers n

For a vector E, which one of the following statements is NOT TRUE?