Question

Let W = {(x,y,z) ∈ R3 : x = z}:

(i) Find a matrix A such that W = {x ∈ R3 : Ax = 0}; and use this to find a basis for W.
(ii) What is the dimension of W?
(iii) Find a non-zero vector perpendicular to W. That is, find
v ∈ R3 such that v.w = 0 for any w ∈ W.

Answer 1

It's first year Uni, Algebra.

Answer 2

@wio