Question

How can we find the solution of a nonhomogeneous system of equations without dealing with the rank of matrices?

(a) Rouche’s theorem

(b) Cramer’s rule

(c) Gauss’s law

(d) Cannot be done

The question was asked during an interview.

My question comes from Linear Systems in chapter Beyond the Basics of MATLAB

Answer 1

Right answer is (b) Cramer’s rule

Best explanation: It is easier to find the solution of a system of equations for a non-homogeneous system using Cramer’s rule. Now, the process is time consuming since we need to find higher order determinants for higher order systems. This is why we go for Rouche’s theorem by hand. But MATLAB computes determinants very fast. Hence, without finding the rank, we can find the solution of a system of nonhomogeneous equations.