## Elementary Linear Algebra 7th Edition

The set $W$ of all $n \times n$ upper triangular matrices is a vector subspace of $M_{n, n}$.
The set $W$ of all $n \times n$ upper triangular matrices is a vector subspace of $M_{n, n}$. Because the sum of two upper triangular matrices is an upper triangular matrix and multiplying any upper triangular matrix by a constant is an upper triangular matrix which means that $W$ is closed under addition and scalar multiplication.