I have this Theorem in my book:
For a Homogeneous System of $m$ Linear Equations in $n$ unknowns, if $m \lt n$, then the system has a non-trivial solution.
I have a confusion about the condition mentioned: Wouldn't it be $n \lt m$ the condition for non-trivial solution? It seems to me that $m \lt n$ is precisely the case we have either only trivial solution or no solution at all.
Best Answer
Hint:
look at.
$2x=0$ with $m=1 , n=1$
and
$2x+y=0$ with $m=1, n=2$
what is the equation with non trivial ( i.e. not null) solution?