Let $V = \text{span}\{(1, 1, 0, 1, 1), (1, 2, 0, 2, 1), (1, 3, 3, 3, 1)\}$ be a subspace of $\mathbb R^5$.
I found using Gram-Schmidt process that the orthonormal basis of $V$ is $\{(0.5 , 0.5 , 0 , 0.5 , 0.5), (-0.5 , 0.5 , 0 , 0.5 , -0.5), (0 , 0 , 1 , 0 , 0)\}$.
Now I am tasked to find a basis of the subspace $V^\perp = \{w ∈ \mathbb R^5\mid w \text{ is orthogonal to }V \}$.
May I ask whether the answer is linked to my orthonormal basis and if it is, what steps do I need to take to obtain the answer?
Thank you.