Question

M2x3 forms a vector space, Does the set N2x3, which consists of all 2x3 matrices with nonnegative entries form a subspace of M2x3? Justify your answer.

Answer 1

Let
\[ \large A=\begin{pmatrix}
1 & 2 & 3\\ 4 & 5 & 6
\end{pmatrix}\in N^{2\times3} \]
and \(\alpha=-1\).
Is \(\alpha A\) still in \(N^{2\times3}\)?