Math Problem Statement
If the determinant of X^2-5I2 is 0, prove that X^2=5I2
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Determinants
Eigenvalues
Diagonalization
Formulas
det(X^2 - 5I_2) = 0
Eigenvalue equation: det(X - λI) = 0
λ^2 = 5
X = PDP^{-1}
X^2 = P D^2 P^{-1} = 5I_2
Theorems
Determinant Theorem
Eigenvalue Theorem
Diagonalization Theorem
Suitable Grade Level
Undergraduate Level (Linear Algebra)
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