Math Problem Statement
L ̊at 𝐴 = 3 −4 0 1 −1 0 −1 3 2 vg ̈or om 𝐴 ̈ar diagonaliserbar. Genom att beräkna egenvärden och egenvektorer
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Eigenvalues
Eigenvectors
Matrix Diagonalization
Formulas
Characteristic equation: det(A - λI) = 0
Quadratic formula: λ = (-b ± √(b² - 4ac)) / 2a
Theorems
Diagonalization theorem: A matrix is diagonalizable if and only if it has enough linearly independent eigenvectors.
Suitable Grade Level
University Level (Linear Algebra)
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