00:01
Hello, so here we're going to use the definition of an orthogonal matrix to find all the orthogonal two by three matrices of the given form, a, b, 0, c, d, 1, e, f, 0.
00:11
So we consider a transpose times a equals the identity.
00:14
So then we're going to have a, c, e, b, d, f, 0, 1 ,0.
00:25
That's going to be a transpose and times a, so times a, b, zero, c, d, 1, e, f, zero, to be equal to the three -by -three identity, so equal to one zero, zero, zero, zero, zero, one.
00:47
And then from there, we multiply that out, and then we obtain the equation that c is equal to zero, d is going to be equal to zero...