Math Problem Statement
If matrix A is n×n and the columns of matrix A are linearly dependent, then the columns cannot span ℝn.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Theory
Linear Independence
Column Space
Dimension
Formulas
Rank(A) ≤ n
dim(Column Space) ≤ n
Theorems
Rank-Nullity Theorem
Linear Dependence and Span Theorem
Suitable Grade Level
College-Level Linear Algebra