Hi there. I started learning about subspaces in linear algebra and I came across a question which i'm unsure how to solve. I understand that there are 'rules' which need to be passed in order for something to be a subspace, but I have no idea how to start with this problem:

Consider the set M23 of all 2 × 3 matrices with real entries under the usual operations of matrix addition and scalar multiplication.

Let

T=([a b c] : a + c= 0 and b + d + f =0)

[d e f]

Prove that T is a subspace of M23

(T is a 2x3 matrix if i made it unclear)

I know that T must contain a zero vector and I know that there must be closer of scalar multiplication and addition.

Can anyone help?