Math Problem Statement

Use determinants to determine whether each of the following sets of vectors is linearly dependent or independent.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Determinants
Linear Independence
Vector Spaces

Formulas

Determinant of a square matrix: det(A)
Criteria for linear independence: If det(A) ≠ 0, the vectors are linearly independent; otherwise, they are dependent

Theorems

Determinant-based Criterion for Linear Independence

Suitable Grade Level

Undergraduate (Linear Algebra Course)

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