Exercise 1.3.12

Question

Prove that the set of $m 	imes n$ upper triangular matrices is a subspace of $\mathrm{M}_{m 	imes n}(F)$.

Jephian C.-H. Lin · Accepted Answer

\begin{proof}
Directly check that sum of two upper triangular matrices and the product of one scalar and one upper triangular matrix are again upper triangular matrices. And of course, the zero matrix is upper triangular.
\end{proof}

Exercise 1.3.12

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Exercise 1.3.12

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