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If and are linearly independent and if is linearly dependent then is in span. a)true b)false

User Daliana
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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.

User Mily
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