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Frequently Asked Questions

How to determine if a vector set is linearly independent?

set of vectors is linearly independent: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero The set is of course dependent if the determinant is zero. Example The vectors <1,2> and <-5,3> are linearly independent since the matrix has a non-zero determinant. Example

Can a single vector be linearly independent?

Note that because a single vector trivially forms by itself a set of linearly independent vectors. Moreover, because otherwise would be linearly independent, a contradiction. Now, can be written as a linear combination of : where are scalars and they are not all zero (otherwise would be zero and hence not an eigenvector).

Are all non-coplanar vectors linearly independent?

Two non-collinear non-zero vectors are always linearly independent . Three coplanar vectors are always linearly dependent. Three non-coplanar non-zero vectors are always linearly independent. More than 3 vectors are always linearly dependent.


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