Math Problem Statement

Verify Cayley Hamilton theorem of the matrix A = [[2, - 1, 2], [- 1, 2, - 1], [1, - 1, 2]]

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrices
Characteristic Polynomial

Formulas

Characteristic Polynomial: p_A(λ) = det(A - λI)
Cayley-Hamilton Theorem: A satisfies its own characteristic equation

Theorems

Cayley-Hamilton Theorem

Suitable Grade Level

Undergraduate (Linear Algebra)