Which of the following subsets of R2 are spanning sets? Explain your answer.(a) {(−1, 0), (0, 1)}, (b) {(−1, 1), (1, −1)}, (c) {(−1, 0), (1, 0), (−1, 1)

Which of the following subsets of R3 are subspaces?(a) The plane of vectors (b1, b2, b3) with b1 = b2.(b) The plane of vectors with b1 = 1.(c) The vectors with b1b2b3 = 0.

Determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span.S = {(−1, 2), (2, −1), (1, 1)}S spans R2.S does not span R2. S spans a line in R2.    S does not span R2. S spans a point in R2.

Define a span and a spanning set. Using the definition of a spanning set, demonstrate that(1, 1, 0), (4, 2, 1), (3, 1, 1) is not a spanning set of R3. In your answer you may use the definitions aspan and a spanning set, but not the concepts of a basis and dimension.

Which of the following sets spans the vector spaceR3? Select all that apply. A. ⎧⎩⎨⎪⎪⎡⎣⎢211⎤⎦⎥,⎡⎣⎢301⎤⎦⎥,⎡⎣⎢512⎤⎦⎥,⎡⎣⎢602⎤⎦⎥⎫⎭⎬⎪⎪ B. ⎧⎩⎨⎪⎪⎡⎣⎢110⎤⎦⎥,⎡⎣⎢300⎤⎦⎥⎫⎭⎬⎪⎪ C. ⎧⎩⎨⎪⎪⎡⎣⎢201⎤⎦⎥,⎡⎣⎢110⎤⎦⎥,⎡⎣⎢001⎤⎦⎥⎫⎭⎬⎪⎪ D. ⎧⎩⎨⎪⎪⎡⎣⎢100⎤⎦⎥,⎡⎣⎢012⎤⎦⎥,⎡⎣⎢003⎤⎦⎥⎫⎭⎬⎪⎪

rove that the set of vectors (1, 2), (3, 4) is linearly independent and spanning in R2