‫Welcome back.
‫Let's find our transfer matrix now, first of all, what we need to do, we need to write this vector,
‫this vector and this vector like this, because if we do that, then we can factor them out.
‫And so if you want to write this vector in terms of this vector, well, then you very simply have a
‫matrix here, a three by three matrix, where you put one here and everything else is zero.
‫So if you write it out, then you will have this vector.
‫So they are equal, right.
‫Similarly, if you want to write this vector in terms of this vector, then you have a matrix here where
‫you have one here and everything else is zero.
‫And finally, if you want to write this vector in terms of this vector, then you very simply have a
‫matrix where you put one here and zeros everywhere else.
‫It makes sense, right?
‫If you write them out, then you will get these vectors here and here and here.
‫And now it just becomes mechanical calculation, so if you rewrite this entire roll like this, where
‫instead of this vector, you write it out like this and instead of this vector, you write it out like
‫this instead of this one, you write it out like this, then this entire row equals the inverse of the
‫transfer matrix times.
‫Again, this vector, which is the same like this, this and this, and now you can factor them out.
‫You can rewrite this entire roll like this where you just put this vector here, and so if you compare
‫this part of the equation to this part of the equation, then since these two vectors are the same,
‫that means that this part here in the parentheses has to be this the inverse of the transfer matrix.
‫And so now you have to take the inverse of this rotation matrix r x, which is the same thing that the
‫transpose of this matrix, because it's an all the normal matrix and the result would be this one and
‫the same thing for this matrix.
‫And if you multiply them together and take their inverse, this is what you need here, then you can
‫rewrite it like this and that would be your result.
‫So this is pure linear algebra here.
‫And then what you need to do, you need to take the inverse of this rotation matrix and multiply it
‫by this green three by three matrix, which is what I did here.
‫And this is the result here.
‫And you also have to take this thing here and multiply it by this purple three by three guy, which
‫is what I did here.
‫And that would be your result here.
‫And now it's very easy to find the inverse of the transfer matrix since you know that it's this row
‫here.
‫Then the first term here will be this one, right.
‫Then the second term here will be this one here, this entire term.
‫And the result of it was here, this matrix.
‫So you just put it here.
‫This is your second term and your third term was this one here.
‫And the result was this matrix here and it's this one.
‫And so now you have the three terms and you add them together.
‫And when you add them together, then this is what you will get.
‫And finally, that's the inverse of your transfer matrix.
‫And if you multiply this matrix by this time, derivative oilor angle vector, then you will get this
‫peak.
‫You are vector.