Consider the provided question,
Given a system of five linear equations in six unknowns are all multiples of one nonzero solution.
It can be written as,
\(Ax=0\) where \(A=5\times6\) matrix
\(dim(NulA)=1\) because all solutions of \(Ax=0\) are multiples of nonzero solution
We have to explain that the system necessarily have a solution for every possible choice of constants on the right sides of the equations.
Since,A is \(5\times6\) matrix \(n=6\)
Image of A is 5 dimensional subspace of \(R^5\) (because A has 5 rows)
This means that Ax=b has a solution for every b