Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Determinants
Matrix Invertibility
Eigenvalues
Row Reduction
Rank of a Matrix

Formulas

Determinant formula for 3x3 matrix
Invertibility condition: Matrix is invertible if determinant ≠ 0
Eigenvalue calculation for 3x3 matrix
Row reduction techniques to find matrix rank

Theorems

Determinant theorem for square matrices
Invertibility criterion for square matrices
Eigenvalue theorem for square matrices
Rank-nullity theorem

Suitable Grade Level

Undergraduate (College Level)