Let a1 =(1, 0,−1), a2 =(0, 1, 0), and a3 =(1, 1,−1). (a) Find scalars c1, c2, c3, so as to write the vector b = (5, 6,−5) as c1a1 + c2a2 + c3a3. (b) Try to repeat part (a) for the vector b = (2, 3, 4). What happens? (c) Can the vectors a1, a2, a3 be used as a basis for R3, instead of i, j, k? Why or why not?
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