Question: Determine whether the statement below is true or false. Justify the answer. If S is a linearly dependent set, then each vector is a linear

Determine whether the statement below is true or false. Justify the answer. If S is a linearly dependent set, then each vector is a linear combination of the other vectors in S Choose the correct answer below 0 A. The statement is false. lfan indexed set of vectors, 8, is linearly dependent. then it is only necessary that one of the vectors is a linear combination of the other vectors in the set. 0 B. The statement is true. If S is linearly dependent then for each j' v], a vector in S, is a linear combination ofthe preceding vectors in S O C. The statement is false. lfS is linearly dependent then there is at least one vector that is not a linear combination of the other vectors, but the others may be linear combinations of each other. 0 D. The statement is true. If an indexed set of vectors, 8, is linearly dependent, then at least one of the vectors can be written as a linear combination of other vectors in the set. Using the basic properties of eq uality. each of the vectors in the linear combination can also be written as a linear combination of those vectors

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