16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 1.6.9

Systems of Linear Equations

Mathematics — Linear Algebra · 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.

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