Math Problem Statement

prove that the matrix is orthogonal

Prove that the matrix P is orthogonal.

Solution

To prove that the matrix PP is orthogonal, we need to show that:

PTP=IP^T P = I

where PTP^T is the transpose of PP, and II is the identity matrix.

Given the matrix ( P

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Theory
Orthogonal Matrices

Formulas

P^T P = I
Matrix Transposition
Identity Matrix

Theorems

Orthogonality Theorem for Matrices

Suitable Grade Level

Grades 11-12, Undergraduate