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Module 1: Vectors in 2 and 3 dimensions

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Linear Dependence and Independence

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XSIQ
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Advanced Mathematics - Linear dependence and independence

Linear dependence and independence

Linear dependence

For two vectors to be linearly dependent, [1] they must be parallel. If
they are dependent, one must be equal to a multiple of the other.

For three or more vectors: if a set of vectors is linearly dependent, then
one vector can be expressed in terms of the other vectors.

If two non-zero vectors are not parallel, they must be linearly
independent.

For three or more vectors to be linearly independent, one of the vectors
cannot be expressed as a linear combination of the other vectors.

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