Math Problem Statement

diagonalise this matrix : [[1,2,3],[3,4,5],[2,32,2]]

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Diagonalization
Eigenvalues
Eigenvectors

Formulas

Characteristic equation: det(A - λI) = 0
Eigenvector equation: (A - λI)v = 0
Diagonalization: A = PDP^{-1}

Theorems

Eigenvalue Theorem
Diagonalizability Theorem

Suitable Grade Level

Undergraduate (Linear Algebra)