Choose two vectors v1, v2 in R^2 and another vector b also in R 2 . Find scalars x, y in R such that xv1 + yv2 = b (if this is not possible, pick other v1, v2, b vectors). Illustrate the vector equation you just solved by graphing the vectors v1, v2, b in the x − y-plane, and be sure to illustrate how b is obtained by adding a scalar of one vector to the other. (2) Repeat part 1 with vectors v1, v2, b in R^3 that give a consistent system. (3) Why is part 2 more difficult than part 1? Explain clearly using complete sentences.
(1) Choose two
v1, v2 are not allowed to be scalar multiples of [1, 0], [0, 1], [1, 0, 0], [0, 1, 0], [0, 0, 1]; neither of the values of x, y is allowed to be -1, 0, or 1 for R^2, and you can have at most one 0, and one 1 of these for R^3. The vectors v1, v2 should be "relatively random looking." Don't over think part (3): a single sentence should be fine.
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