I'm trying to find an orthonormal basis for the subspace $\displaystyle \mathbf{R}^3$ consisint of all vectors (a,b,c) such that a+b+2c=0. Can I use Gram Schmidt? I don't know what to do about the constraint?
I'm trying to find an orthonormal basis for the subspace $\displaystyle \mathbf{R}^3$ consisint of all vectors (a,b,c) such that a+b+2c=0. Can I use Gram Schmidt? I don't know what to do about the constraint?
Well, before you can use "Gram-Schmidt" to find an orthonormal basis, you have to have a basis!
From a+ b+ 2c, you can get a= -b- 2c so (a, b, c)= (-b- 2c, b, c)= b(-1, 1, 0)+ c(-2, 0, 1). Do you see the two basis vectors? Use Gram-Schmidt on them.