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Let \(V, W\) be two-dimensional real vector spaces, and let \(f_{1}, \ldots, f_{5}\) be linear transformations from \(V\) to \(W\).

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Let \(V, W\) be two-dimensional real vector spaces, and let \(f_{1}, \ldots, f_{5}\) be linear transformations from \(V\) to \(W\). Show that there exist real numbers \(a_{1}, \ldots, a_{5}\), not all zero, such that \(a_{1} f_{1}+\cdots+a_{5} f_{5}\) is the zero transformation.
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