Question

For a homogeneous system, Cramer’s rule will always yield a trivial solution in MATLAB.

(a) True

(b) False

I have been asked this question during an interview for a job.

This interesting question is from Linear Systems in portion Beyond the Basics of MATLAB

Answer 1

The correct option is (a) True

To explain I would say: The process of Cramer’s rule will always yield a solution for the variables in a system. But for a homogeneous system with no constant value, it will yield a 0 as a solution. Hence all the variables will get a 0 as a solution, there-by yielding a trivial solution. This doesn’t imply that the system is inconsistent- this is why we go for comparing ranks, it will allow us to establish a more pertinent justification of the nature of the system.