Final answer:
Without specific vectors provided, it is impossible to determine if 'F' and 'C' are linearly independent. A set of vectors is linearly independent if no vector can be written as a combination of others, but since the vectors are not given, we cannot assess this.
Step-by-step explanation:
To determine if vectors are linearly independent, you must first have the vectors in question. The original prompt does not include specific vectors to analyze, which makes it impossible to answer the question of whether they are linearly independent or not. In general, a set of vectors is considered linearly independent if no vector in the set can be written as a linear combination of the others. In the context of this problem, you would typically set up a matrix containing the vectors and perform operations to determine if the matrix is of full rank, implying linear independence, or if a row reduces to zero, implying linear dependence.
If 'F' and 'C' are placeholders for vectors, you would still need the actual vectors to apply these concepts. The information given does not allow a definitive answer to be drawn; hence, the answer is Cannot be determined based on the information provided.