Find the dimension of the subspace $V$ of $\mathbb{R} ^4$ that is generated by the vectors $(0,1,0,1),(1,0,1,0),(1,1,1,1)$.

Question

• Find the dimension of the subspace $V$ of $\mathbb{R} ^4$ that is generated by the vectors $(0,1,0,1),(1,0,1,0),(1,1,1,1)$.

My answer is $2$ because $(1,1,1,1)=1(0,1,0,1)+1(1,0,1,0)$ and there are two basis: $(0,1,0,1),(1,0,1,0)$.

Can you check my answer?

Answer 1

Your answer is correct, but you need to check if the vectors $(0,1,0,1)$ and $(1,0,1,0)$ are independent too.