characterization of basis of finite dimensional vector space

Let $X$ be a linear space and let ${\varphi }_i$ be the linear functional, ${\varphi }_i:X\to ℝ,1\le i\le n$, such as$[{\varphi }_i(\upsilon )=0,\forall i=1,2,\mathrm{\dots },n]\to [\varphi (\upsilon )=0].$Then there exist ${\lambda }_1,{\lambda }_2,\mathrm{\dots },{\lambda }_n\in ℝ$ such as $\varphi ={\sum }_{i=1}^n{\lambda }_i{\varphi }_i$.