00:01
Have the given quadratic form that is 3 x1 squared minus 2 x2 minus 2 x2 squared squared plus 5 x3 squared plus 4 x1 sorry x2 x2 x2 x2 x3 yeah oh no it's just x1 x1 x2 sorry it oh no it's just x1 x2 x1, x2, minus 6, x1, x3.
01:03
Okay, so the matrix we're considering in this problem is a 3x3 matrix.
01:09
So let's suppose the matrix is a, b, c, d, e, f, g, h, i.
01:26
Alright.
01:26
All right.
01:28
So the way we figure this out is just to first, just use x1, x to x3 and this matrix to find out the general quadratic form.
01:43
So that's x1, x2, x3, and a, b, c, d, e, f, g, h, sorry, have the h, i.
02:04
Okay, and we also have a column vector.
02:16
X2 and x3.
02:22
Okay, so by taking the product of these three matrices, we finally get, i'll just write down the answer here because it's just a matrix multiplication.
02:36
I think i believe every one of you can solve this.
02:39
So it's just a x1 squared plus e x2 squared plus n i x3 squared plus b plus d x1 x2 plus g plus c x1 x3 and we have h plus f x2 x2.
03:26
Plus f and x2 x3...