Decide by inspection whether the set of vectors is linearly dependent or linearl

Question

Decide by inspection whether the set of vectors is linearly dependent or linearly independent and select the first reason why from the options listed below. {(2 0 2 -1), (2 2 0 1), (4 2 2 0)} There are more vectors than the number of components per vector. The 0 vector is in the set. The vectors are not scalar multiples of one another. The matrix whose columns are the given vectors has a pivot element in every column. There are fewer columns than the number of components per vector. One of the vectors is a scalar multiple of another vector in the set. One of the vectors is a linear combination of the other vectors in the set. The vectors are scalar multiples of one another.

Explanation / Answer

The given vectors are linearly dependent because one vector (column 3 )

can be written as the combination of column 1 and column 2

(7th point )

C = A +B

A B C Are column vectors 1 2 and 3

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