Respuesta :
The statement "if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s" is false.
What is the linearly dependent set?
A vector set's linear independence is an important attribute. If no vector in a set can be written as a linear combination of the other vectors in the set, the set is said to be linearly independent. The set is said to be linearly dependent if any of the vectors can be represented as a linear combination of the others.
If S is a linearly dependent set, then each vector in S is a linear combination of the others.
This is false.
For example, v₁ = (1,0), v₂ = (2,0), and v₃ = (1,1). Then v₂ = 2v₁ but v₃ is not a linear combination of v₁ and v₂, since it is not a multiple of v₁. But 2v₁ - 1v₂ + 0 v₃ = 0.
If an indexed set of vector S is linear dependent, then it is only necessary that one of the vectors is in the set.
Hence, the correct answer would be option (B).
To learn more about linearly dependent set here:
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