MATH 3000 Quiz: MATH 331 Mizzou Quiz 6 Solutions
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Oct. 3, 2003: (4 points) let {v1, . , vn} be a set of vectors in the vector space v . , vn} is linearly independent if the only way to have c1v1 + + cnvn = 0 is to have c1 = = cn = 0. Comments: 1) a correct answer does not only address the question when v = rm: the only in the answer is critical. Without it, you will nd that every set of vectors ful lls the condition: in r3, let v1 = [ 1, (8 points) is [ 1. If so, nd a linear combination of v1, v2, v3. 3 ]t , and v3 = [ 1. 5 ]t = a1v1 +a2v2 +a3v3 for some a1, a2, a3 r. solving. For (a) you want to see if [ 1 this equation gives the augmented matrix below, which can then be row-reduced as shown:
