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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?