asked 90.1k views
3 votes
If and are linearly independent and if is linearly dependent then is in span. a)true b)false

asked
User Daliana
by
8.6k points

1 Answer

6 votes

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.

answered
User Mily
by
8.2k points
Welcome to Qamnty — a place to ask, share, and grow together. Join our community and get real answers from real people.