The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.

A set of vectors is linearly dependent if and only if one of the vectors is in the span of the other ones. Any such vector may be removed without affecting the span.

This page covers the concepts of linear independence and dependence among vectors, defining linear independence as having only the trivial zero solution in equations.

Aug 8, 2025 · Linear independence is a fundamental concept of linear algebra. It has numerous applications in fields like physics, engineering, and computer science. It is necessary for determining …

Remember a set of vectors is linearly independent if the only way to take a linear combination of the vectors, and get the zero vector out, is to take 0 as all of the coefficients.

There now follow a couple of statements which can be helpful in determining whether a given set of vectors is linearly dependent or not. The first one tells us that an ordered set is linearly dependent …

A set of vectors is called linearly dependent if one of the vectors is a linear combination of the others. Otherwise, the set of vectors is called linearly independent.

Linear independence is a property of sets of vectors that tells whether or not any of the vectors can be expressed in terms of the other vectors (and any scalars).

Definition and explanation of the concepts of linear dependence and independence, with examples and solved exercises.

A set of nonzero weights that yield zero is called a linear dependence relation among \ (\ { {\bf v_1, ..., v_p}\}\). A set of vectors is linearly dependent if and only if it is not linearly independent.