Math Problem Statement

a) Show that the matrix for the following quadratic form is positive definite √ 3x21 + 2x22 − 2 2 x1 x2

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Quadratic Forms
Positive Definite Matrices

Formulas

Quadratic form matrix representation: Q(x) = x^T * A * x
Determinant formula for 2x2 matrix: det(A) = ad - bc

Theorems

Positive Definiteness Criterion: A matrix is positive definite if all leading principal minors are positive.
Eigenvalue Criterion: A matrix is positive definite if all eigenvalues are positive.

Suitable Grade Level

Undergraduate