00:01
Hello there, so in this occasion we need to compute this determinant to show that is equals to the right -hand side of this equation.
00:09
Okay, so let's take this determinant.
00:21
Okay, so we got here this determinant, and i'm going to use the expansion by co -factors to complete the determinant.
00:28
So let's start with this one here.
00:30
So is 1 times v .a minor that corresponds to y, y, square, z, z, z.
00:38
Square.
00:40
Then the second entry of this matrix is a minus 1 because it's on this position, and the summation of the indices of that position is off, so that's why i'm adding here a minus 1.
00:54
And the minor in this case is x, x squared, z, z squared.
01:00
And the last one is this one here, so it's plus 1 and the minor that corresponds to x, x squared y, y, square.
01:10
So i after computing this determinant here, we obtain that b is the determinant of this 3x3 matrix is equal to z squared y minus y square z minus here x z squared minus x squared minus x squared z and plus x y square minus x square y.
01:50
Okay, so we got this here.
01:53
And now i'm going to take some common factors.
01:57
So the first i'm going to focus on the z square here...