Kunze Linear Algebra · Problem 1.6.9

Systems of Linear Equations

Mathematics — Methods · upper-triangular-matrices

Problem

n \times n

matrix

A

is called upper-triangular if

A_{ij} = 0

for

i > j

, that is, if every entry below the main diagonal is

0

. Prove that an upper-triangular (square) matrix is invertible if and only if every entry on its main diagonal is different from

0