Vectors, Matrices & Graphical Effects
Vectors
Movement
3D vectors are ordered like so:
\[\langle x,y,z\rangle\]With $z$ being the vertical component.
In 4D a 4$^{th}$ dimension is used for time:
\[\langle x,y,z,t\rangle\]Size
Here is an example:
\[\vert\vert\langle1,-2,2,-4\rangle\vert\vert\]You will generally be expected to find the euclidean distance.
This example will give:
\[\sqrt{25}=5\]Spaces
Suppose you are given the following collection:
\[S=\{\langle p,q,r\rangle\in\Bbb Z ^3_8:p^q=q^r\}\]Three vectors from the set of integers with modulo 8. When we take the first component and raise it to the power of the second modulo 8 we get the same as the second and third
\[H=\Bbb Z_8=\{0,1,2,3,4,5,6,7\}\]- $S$ is closed under scalar multiplication - False
- $S$ is not closed under addition. - True
- $S$ contains $\langle0,1,1\rangle$. - False
- $S$ is a vector space. - False
- $S$ does not contain $\langle1,1,0\rangle$. - False
Matrices
You can’t implement translation using a $2\times2$ vector. Scaling and rotation you can.
Example Questions
Polynomials and Properties
- Degree 3 and $2x^2$.
- Degree 4 and $4x^2$.
- Degree 4 and $0x^2$.