For the system     The value of a for which system must not be controllable is ___Select one:a. 0b. -3c. 1d. 3

To determine the value of 'a' for which the system must not be controllable, we need to analyze the controllability condition. The controllability matrix for a system is given by:

C = [B, AB, A^2B, ..., A^(n-1)B]

where A is the system matrix and B is the input matrix. The system is controllable if and only if the rank of the controllability matrix is equal to the number of states of the system.

In this case, the system is not controllable if the rank of the controllability matrix is less than the number of states. Let's calculate the controllability matrix for the given system:

A = [a] B = [1]

C = [B, AB] = [1, a]

The rank of the controllability matrix is 1 if 'a' is not equal to 0, and it is 2 if 'a' is equal to 0. Therefore, the value of 'a' for which the system must not be controllable is a. 0.

So, the correct answer is a. 0.