differentiating determinants...

Chewwy

17

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OP

maths is no laughing matter.

Reply 3

Morbo

17

I don't really understand what you want to do. Find the determinant of both those matrices, and then do the derviatives on the left hand side, and you should come out with that identity it gives you. Do you not know how to do a determinant? Or do you not know how to differentiate?

Reply 4

Chewwy

OP

17

Worzo

I don't really understand what you want to do. Find the determinant of both those matrices, and then do the derviatives on the left hand side, and you should come out with that identity it gives you. Do you not know how to do a determinant? Or do you not know how to differentiate?

i just keep going wrong. oh well, i'll keep trying. there's one more i'm stuck on...

a triangle is formed by the lines a_1 x + b_1 y + c_1 = 0, a_2 x + b_2 y + c_2 = 0, a_3 x + b_3 y + c_3 = 0. show the area of the triangle = Δ^2 / 2C_1.C_2.C_3

where C_n denotes the cofactor of c_n

Reply 5

El Matematico

For your original question, I find the determinant to be:

yz^2 - zy^2 - xz^2 + zx^2 + xy^2 - yx^2

So finding the partial derivative WRT y, gives

z^2 - 2zy +2xy - x^2

Then finding the partial derivative WRT x gives

2y - 2x

Which you can put back into matrix format.

differentiating determinants...

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