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

Ishaan Booker

Answered question

2022-07-15

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?

Answer & Explanation

akademiks1989rz

akademiks1989rz

Beginner2022-07-16Added 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.
PoentWeptgj

PoentWeptgj

Beginner2022-07-17Added 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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