Find a basis for the subspace?

Question

I'm trying to figure out the basis for the plane with equation 3x - 2y + 5z=0. The answer is supposed to be (2/3, 1, 0) and (-5/3, 0, 1), but I'm not sure how to get it.

Answer 1

Best Answer - Chosen by Asker

Of course since you have one equation and three unknowns there is no unique solution. from the two answers that you have,
the first set z = 0 and y = 1
the second set y = 0 and z = 1 so following with that logic
the third set x = 0 and either z = 1 or y = 1 Your choice.

Asker's Rating:

Asker's Comment:

Thanks