00:01
We're given two vectors in r4, u and v.
00:05
And actually if we look at these vectors we can see that they're not proportional, so they are linearly independent.
00:15
We'll call w the subspace of r4 that's spanned by v and u.
00:24
We want to find w perpendicular, this perpendicular space to w.
00:30
So that's going to be spanned by two vectors that are perpendicular to both u and v.
00:36
So let's define a vector called little w, which is a, b, c, d.
00:48
And because they have to be orthogonal, that means their dot products have to be zero with u and v.
00:57
So we have to satisfy these two equations for a, b, c, and d.
01:03
And any two solutions will work as long as they're linearly independent of each other.
01:12
So let's solve the second equation for a.
01:15
So if i know b, c, and d, i can find a and then plug that back into the first equation and then simplify it...