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.
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?