Final answer:
A linearly dependent vector is always in the span of the linearly independent vectors.
Step-by-step explanation:
Given that F and C are linearly independent and that A is linearly dependent, we can say that A can be expressed as a linear combination of F and C. This means that A is in the span of F and C.To prove this, let's assume that A = k1F + k2C, where k1 and k2 are scalars. Since F and C are linearly independent, k1 and k2 must not both be zero for A to be in the span of F and C.Therefore, the statement 'A is in span' is true.