This is a task from a test exam you can find here (in German): http://docdro.id/QRtdXkM
Is the following statement true or false?
Every real homogeneous linear system of equation that has more than one solution, has infinite solutions.
I think the statement is true because a linear system of equations can only have either one solution, no solution or infinite solutions. This statement clearly says "more than one solution $\rightarrow$ infinite solutions" which is true.
Is it really correct like that or there is some special case which can make this statement false?