Question
Let $S=\{\mathbf{u}, \mathbf{v}\}$ be a linearly independent set. Prove that the set $\{\mathbf{u}+\mathbf{v}, \mathbf{u}-\mathbf{v}\}$ is linearly independent.
Step 1
Step 1: Assume that there exist scalars $c_1$ and $c_2$ such that $c_1(\mathbf{u}+\mathbf{v}) + c_2(\mathbf{u}-\mathbf{v}) = \mathbf{0}$. Show more…
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