Let $F$ be a field such that it has a finite non-Galois extension field. Let $V$ be a finite-dimensional vector-space over $F$. Let $V _ { 1 } , \ldots , V _ { r }$ be proper subspaces of $V$. Prove or disprove the following assertion: $V \neq \bigcup _ { i = 1 } ^ { r } V _ { i }$.