Let v_1,...,v_n be linealy independent vectors in RR^m and let w=a_1v_1+...+a_nv_n with real numbers a_1,...a_n, be linear combination of these vectors. Prove if a_1 != 0, then the vector w,v_2,...,v_n are linearly independent So far, what I have thought is forming a formula like this: x_1w+x_2v_2+...+x_nv_n=0, because v_1,...,v_n is linearly independent vectors, so x_2=...=x_n=0, then now we need to prove x_1=0 so these vector will be linearly independent. But from here, I don't know how to process further more in this problem, can anyone help me out with a way to solve this or a better alternative solution is appreciate.

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