I was given a question related to finding a $\lambda$ value for a homogeneous system of linear equations not to have any solution. This $\lambda$ was among the coefficients matrix (if considering the matrix form of the system $AX=0$).
I immediately thought of the affirmation that is it not possible because for any given homogeneous system it will always have the trivial solution $X=0$.
My question: My affirmation is true? and if so, Is there a way to prove it or is something completely unnecessary and pointless?
Thanks in advance