If three vectors are on the z-x plane and the fourth vector is not in this plane, the vectors would be linearly independent, no?

Ishaan Booker 2022-07-15 Answered
Are four non zero vectors are always linearly dependant
If three vectors are on the z-x plane and the fourth vector is not in this plane, the vectors would be linearly independent, no?
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Answers (2)

akademiks1989rz
Answered 2022-07-16 Author has 16 answers
No, in general, four non-zero vectors are not always linearly dependant. For example, the vectors [ 1 0 0 0 ] , [ 0 1 0 0 ] , [ 0 0 1 0 ] , [ 0 0 0 1 ] are linearly independent.
However, in R 3 , it is indeed true that any set of four vectors is linearly dependent.

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PoentWeptgj
Answered 2022-07-17 Author has 6 answers
If 3 non-zero vectors are in the z−x plane, one of the vector can be expressed as linear combination of the other two.
It is linearly dependent.

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