A First Course in Linear Algebra · Problem T20

Vector Spaces — Robert Beezer

Mathematics — Linear Algebra · subspace-upper-triangular

Problem

A square matrix

A

of size

n

is upper triangular if

[A]_{ij} = 0

whenever

i > j

. Let

UT_n

be the set of all upper triangular matrices of size

n

. Prove that

UT_n

is a subspace of the vector space of all square matrices of size

n

M_{nn}