Math Problem Statement
Determine the nature,index and signature of the quadratic form 𝑥1 2 + 5𝑥2 2 + 𝑥3 2 + 2𝑥2𝑥3 + 6𝑥3𝑥1 + 2𝑥1𝑥2.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Quadratic Forms
Eigenvalues
Matrices
Formulas
Q(\mathbf{x}) = \mathbf{x}^T A \mathbf{x}
\det(A - \lambda I) = 0
Theorems
Sylvester's Law of Inertia
Diagonalization of Symmetric Matrices
Suitable Grade Level
Undergraduate (Linear Algebra)
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