a) Determine whether S = {(1,0, -1), (2,1,0), (3,1,-1), (1,1,1)} spans. R³. b) Find all c E R for which S = {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly independent set of vectors in R³. c) Determine whether W = {(x, y, z) € R³| x² + y² = z²} is a subspace of R³.

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A: Hi, thank you for the question. Since you have posted multiple questions, as per our policy we…

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