I have the set : $$W=[(x_1,x_2,x_3,x_4)\in{\mathbb{R}^4}\quad| \quad x_1-x_2-x_3-x_4=0]$$
I need to find orthonormal basis, So I found just one vector and I have only parameters in my answer and I am not sure that what suppose to be. I found the vector $$\vec\epsilon_1= \frac{1}{\sqrt(x_2+x_3+x_4)^2 +x_2^2+x_3^2+x_4^2}(x_2+x_3+x_4,x_2,x_3,x_4)$$
My question is, should I get an answer with numbers?
Hint: To begin, find any basis for $W$. If you want to do so by using a familiar technique, it might be helpful to note that $W$ is the kernel/nullspace of the matrix $A = \pmatrix{1&-1&-1&-1}$. Once you have a basis, you can apply the Gram-Schmidt process to produce an orthonormal basis of $W$.