Math Problem Statement

  1. Reduce the quadratic form 2x2+2y2+2z2-2xy-2yz-2xz to canonical form by an orthogonal transformation and hence find rank, index and nature of the quadratic form

Solution

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Math Problem Analysis

Mathematical Concepts

Quadratic Forms
Matrix Diagonalization
Eigenvalues and Eigenvectors

Formulas

Quadratic form matrix representation Q(x, y, z) = [x y z] * A * [x y z]^T
Characteristic equation: det(A - λI) = 0

Theorems

Eigenvalue Theorem
Diagonalization of Symmetric Matrices

Suitable Grade Level

Undergraduate Mathematics