Show that the set W consisting of all vectors in R4 that are orthogonal to both X and Y is a subspace of R4. Here X and Y are vectors such that X = (1001) and Y = (1010).
Part b) Find a basis for W.
The Attempt at a Solution
So I know to satisfy being a subspace we have to satisfy scalar multiplication, and vector addition, and the zero vector has to be in the space. How do I set up the conditions of the space though? Are all the vectors orthogonal to these two going to be those such that c1X + c2Y = 0 only has c1,c2 = 0 as a solution?
The second part I know works off of the first. I was really just hoping someone could point me in the right direction. Thanks!