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1) Let S={v_1, ..., v_p} be a linearly dependent set of vectors in R^n. Explain why...

1) Let S={v_1, ..., v_p} be a linearly dependent set of vectors in R^n. Explain why it is the case that if v_1=0, then v_1 is a trivial combination of the other vectors in S.

2) Let S={(0,1,2),(8,8,16),(1,1,2)} be a set of column vectors in R^3. This set is linearly dependent. Label each vector in S with one of v_1, v_2, v_3 and find constants, c_1, c_2, c_3 such that c_1v_1+ c_2v_2+ c_3v_3=0. Further, identify the value j and v_j (as in the proof of the result) and write v_j as a linear combination of the vectors v_1, ..., v_(j-1) as done in the proof. You may need to relabel the vectors to do this!.

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