Linear Algebra and Differential Equations
Linear dependence occurs when a set of vectors can be expressed as a linear combination of other vectors in the set, meaning at least one vector in the set can be written as a combination of the others. This concept is crucial for understanding the properties of vector spaces and directly relates to the evaluation of determinants, as a set of linearly dependent vectors leads to a determinant value of zero, indicating that the vectors do not span the space.
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