Question
If $\left\{v_{1}, v_{2}, \ldots, v_{n}\right\}$ is a linearly dependent set of vectors, prove that one of these vectors is a linear combination of the other.
Step 1
Since the set of vectors is linearly dependent, there exists a non-trivial linear combination of these vectors that equals the zero vector. In other words, there exist scalars c_1, c_2, ..., c_n, not all zero, such that: c_1 * v_1 + c_2 * v_2 + ... + c_n * v_n = Show more…
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