![]() Step 3: Now find the transpose of the matrix which comes from after Step 2. ![]() Step 2: Create another matrix with the cofactors as its elements. see below the steps, Step 1: Find the Cofactor of each element present in the matrix. Dn(t) represent given matrix functions of the real variable /, and y. To find the Adjoint of a Matrix, first, we have to find the Cofactor of each element, and then find 2 more steps. Next we define a sequence of stopping times: First \( \tau_0 = 0 \) and \( \tau_1 = \tau\). of linear differential-difference equations). Finally, if \( \lambda(x) = 0 \) then \( x \) is an absorbing state, so that \( \P(\tau = \infty \mid X_0 = x) = 1 \). On the other hand, if \( \lambda(x) \in (0, \infty) \) then \( x \) is a stable state, so that \( \tau \) has a proper exponential distribution given \( X_0 = x \) with \( \P(0 \lt \tau \lt \infty \mid X_0 = x) = 1 \). The assumption of right continuity rules out the pathological possibility that \( \lambda(x) = \infty \), which would mean that \( x \) is an instantaneous state so that \( \P(\tau = 0 \mid X_0 = x) = 1 \). In the case of inherent discrete-timesystems, the matrix may be singular in general. \) implies the memoryless property of \( \tau \), and hence the distribution of \( \tau \) given \( X_0 = x \) is exponential with parameter \( \lambda(x) \in [0, \infty) \) for each \( x \in S \). It is important to point out that the discrete-timestate transition matrix may be singular, which follows from the fact that b is nonsingular if and only if the matrix is nonsingular.
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