Suppose q1, q2, a3 are linearly independent vectors. q1 and q2 are already orthonormal. Give a formula for a third orthonormal vector
q3 as a linear combination of q1, q2, a3.
I have no idea where to even start with this one

Question

mathmate · Answer

Are we in real or complex?

anonymous · Answer

real

mathmate · Answer

You'd use Gram-Schmidt process, which for this case where q1 and q2 are orthonormal x3=a3 -q1 -q2 After that, you'd normalize x3 to become q3.

anonymous · Answer

I didnt even think about that thanks! So then given that, the answer Ive come up with is Q3=(a3-Q1Q1^Ta3-Q2Q2^Ta3)/II "               " II

mathmate · Answer

Yep, something along those lines, not too sure about your notations.
I forgot to mention <a3,q1> is the inner product, and for real, it's simply the dot-product.