a) The vectors (1, 0) and (0, 1) are linearly independent because you cannot multiply one vector by a scalar to obtain the other vector.
b) The vectors (-1, 1, 0) and (0, 1, 2) are linearly independent because you cannot multiply one vector by a scalar to obtain the other vector.
c) The vectors (0, 1, 1), (0, 2, 1), and (1, 5, 3) are linearly independent. One way to prove this is to form a matrix with the vectors as columns and row reduce it. If the row-reduced matrix has a row of zeros, then the vectors are linearly dependent. However, in this case, the row-reduced matrix does not have a row of zeros. Therefore, the vectors are linearly independent.
Decide whether the following vectors are linearly independent or not (on ()
a) ((, 0) and (0, 1)
b) (-1, 1, 0) and (0, 1, 2)
c) (0, 1, 1), (0, 2, 1), and (1, 5, 3)
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