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**superdude** Suppose that $\displaystyle {\mathbf{v}_1,\mathbf{v}_2...\mathbf{v}_k}$ is linearly independent oset of vectors in $\displaystyle \mathbb{R}^n$. Show that if A is an nxn nonsingular matrix then $\displaystyle {A\mathbf{v}_1,A\mathbf{v}_2...A\mathbf{v}_k}$ is also linearly independent.

So if the given set is linearlly independent that means that $\displaystyle c_1 \mathbf{v}_1+c_2 \mathbf{v}_2+...+c_k \mathbf{v}_k=\mathbf{0}$

and that $\displaystyle c_1=c_2=...=c_k=0$

doesn't that mean that A must be 0?

can I use the theorem that if the larger set is linearally independent then it's subspace must be linearally independent? I'm not sure if I can use this becuse it's not like Av is part of the original set of vectors.