Tagged Questions
2
votes
3answers
130 views
On integral of a function over a simplex
Help w/the following general calculation and references would be appreciated.
Let $ABC$ be a triangle in the plane.
Then for any linear function of two variables $u$.
$$
\int_{\triangle}|\nabla ...
3
votes
2answers
116 views
Parallelogram area using determinant
Given a Parallelogram with the co-ordinates: $(a+c, b+d), (c,d), (a, b)$ and $(0, 0)$
I have to prove that the area of the Parallelogram is:
$|ad-bc|$ as in the determinant of:
$$\begin{bmatrix}
a ...
4
votes
1answer
29 views
Determinant of the matrix $D_n(2,3,1)$
The matrix $D_n(2,3,1)$ is to be written in the form
$$\pmatrix{3 & 1 & 0 & 0 & ... & 0 \\ 2 & 3 & 1 & 0 & ... & 0 \\ 0 & 2 & 3 & 1 &... ...
1
vote
2answers
88 views
How to workout the determinant of the matrix $D_n(\alpha, \beta, \gamma)$.
I am going through an example in my lecture notes. This is it:
Let's introduce the matrix $D_n(\alpha, \beta, \gamma)$, which looks like this:
$$\pmatrix{\beta & \gamma & 0 & 0 ...
2
votes
1answer
106 views
Some Questions on Determinants and Geometry
For real valued matrices, I know that the absolute value of the determinant is equivalent to the volume of the vectors forming the parallelepiped in the matrix.
Suppose that $A$ and $B$ are real ...
1
vote
1answer
85 views
Given a parallelepiped, how do I find the determinant given vertices?
Here are the given vertices of a given parallelepiped...
$ (-1, 0, 0), (0, 4, 0), (-3, -5, 2), (-2, 2, -1) $
I know that first, we should translate all to the origin...
$ (0, 0, 0), (1, 4, 0), (-2, ...
1
vote
2answers
196 views
Determinant form of equation, 3 variables, third order (nomogram)
I'm trying to put the following equation in determinant form:
$12h^3 - 6ah^2 + ha^2 - V = 0$, where $h, a, V$ are variables (this is a volume for a pyramid frustum with $1:3$ slope, $h$ is the height ...
1
vote
1answer
226 views
Meaning of this 4x4 determinant
Let $p,q,r$ and $s$ be four points on the plane. Moreover, $p,q,r$ are given in clockwise order. My book said that the following determinant is positive if and only if $s$ lies inside the circle ...
0
votes
1answer
263 views
volume of a parallelogram [duplicate]
Possible Duplicate:
Determinants and volume of parallelotopes
Can you give me a direction about how to prove that $|det(UVW)|$ is the 3D volume of the parallelogram that defined by $U, V$ ...
3
votes
2answers
146 views
How do I prove that the following method to find whether a point lies within a polygon is correct?
I came across the following method to determine whether a given point lies inside a convex polygon - however, I'm not sure how to prove it.
Given any three points on the plane $(x_0,y_0)$, ...
