Let a1 = (1, 1) and a2 = (1,−1). (a) Write the vector b = (3, 1) as c1a1 + c2a2, where c1 and c2 are appropriate scalars. (b) Repeat part (a) for the vector b = (3,−5). (c) Show that any vector b = (b1, b2) in R2 may be written in the form c1a1 + c2a2 for appropriate choices of the scalars c1, c2. (This shows that a1 and a2 form a basis for R2 that can be used instead of i and j.)
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