Math Problem Statement

L ̊at A =  1 1 1 1 1 1 1 1 1  . Best ̈am alla egenv ̈arden och motsvarande egenrum till A. Finns det en bas f ̈or R3 som best ̊ar av egenvektorer till A? Best ̈am, om m ̈ojligt en matris P och en diagonal matris D s ̊a att D = P −1AP

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Eigenvalues
Eigenvectors
Matrix Diagonalization

Formulas

Characteristic equation: det(A - λI) = 0
Matrix diagonalization: D = P^{-1} A P

Theorems

Eigenvalue decomposition
Diagonalization theorem

Suitable Grade Level

University level (Linear Algebra course)