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Under what conditions on a, b, c will vector v=[a,b,c] belong to

span {[1,-1,3],[3,-2,7],[1,1,-1]}

I don't understand how to find the span

Based on the previous Q&A, we can determine if the vectors listed are linearly independent, and thus span 3-D and contain v, if the determinant of the matrix of the vectors is zero. The calculation reveals that det ≠ 0. So we can write, for instance,

c1a + c2b = c

where c1 and c2 are constants i.e., c is a linear combination of a and b. This condition can also be written equivalently as c3b + c4c + a or c5a + c6c = b.

Randy

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