Homework SourseLet W be the set of all vectorsx y x y with x and y real Fin
Let W be the set of all vectors[x y x+ y] with x and y real. Find a basis of W^1 ![Let W be the set of all vectors[x y x+ y] with x and y real. Find a basis of W^1 SolutionCompute the inner product of v with an arbitrary vector from W. If you](/WebImages/41/let-w-be-the-set-of-all-vectorsx-y-x-y-with-x-and-y-real-fin-1127600-1761601624-0.webp "Let W be the set of all vectors[x y x+ y] with x and y real. Find a basis of W^1 SolutionCompute the inner product of v with an arbitrary vector from W. If you")
Solution
Compute the inner product of v with an arbitrary vector from W. If you get zero independent of the components x and y, then v is in W perp.
1) v.w = -x - y + (x + y) = 0, for all x and y
2) v.w = -2x - 7y + 11(x + y) = 9x + 4y, which is only zero for some values of x and y
3) v.w = -2x - 2y + 2(x + y) = 0 for all x and y
