Math Problem Statement

Prove that an n × n upper triangular matrix is invertible if and only if all of its diagonal entries are non-zero. 2

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Theory
Invertibility
Determinants

Formulas

det(A) = a_{11} * a_{22} * ... * a_{nn} (for upper triangular matrix)
A matrix is invertible if and only if det(A) ≠ 0

Theorems

Determinant of Upper Triangular Matrix
Invertibility Criterion (det(A) ≠ 0)

Suitable Grade Level

Undergraduate - Linear Algebra