I'm not quite sure how do this question and would appreciate any help.
Recall that we denote $M_{2\times2}$ the set of $2 \times 2$ matrices, with real entries. Recall also that $M_{2\times2}$ is a vector space under the usual addition and scalar multiplication of functions. We denote by
$$T = \begin{pmatrix} a & b \\\ 0 & c \end{pmatrix}, a, b, c \in \mathbb{R}$$
the set of upper triangular matrices in $M_{2\times2}$. Prove that $T$ is a subspace of $M_{2\times2}$.
How can I solve this question?
Hint:
you have simply to prove that the addition of two matrices of $T$ is a matrix of $T$ and the product of a scalar (a real number) for a matrix of $T$ gives a matrix of $T$ . It's really simple !