Question: Determine whether the statement below is true or false. Justify the answer. If a set contains fewer vectors than there are entries in the vectors,

Determine whether the statement below is true or false. Justify the answer. If a set contains fewer vectors than there are entries in the vectors, then the set is linearly independent Choose the correct answer below. 0 A. The statement is true. If a set contains fewer vectors than there are entries in the vectors, then there are less variables than equations, so there cannot be any free variables in the equation Ax = 0. O B. The statement is true. There exists a set that contains fewer vectors than there are entries in the vectors that is linearly independent. One example is a set consisting of two vectors where one of the vectors is not a scalar multiple of the other vector. 0 C. The statement is false. There exists a set that contains fewer vectors than there are entries in the vectors that is linearly dependent. One example is a set consisting of two vectors where one of the vectors is a scalar multiple of the other vector. 0 D. The statement is false. Aset of vectors is linearly independent if none ofthe vectors can be written as a linear combination of the others. lfthere are fewer vectors than entries in the vectors, then at least one of the vectors must be written as a linear combination of the others

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