Set of Polynomials divided by single linear factor is linearly independent – math.stackexchange.com

Let $f(t)$ be a polynomial composed of linear factors $(t-a_i)$ for $i \in [n]$, i.e $f(t) = (t-a_1)\cdots (t-a_n) $. Let $g_k(t)$ be given by: $$g_k(t) = \frac{f(t)}{(t-a_k)}$$ for $k \in[n]$. Prove ...

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