Math Examples

From FUKTwiki

These are examples. For more extensive help, see metawikipedia:Help:Displaying_a_formula.

$a 1 x + b 1 y = c 1$
$a 2 x + b 2 y = c 2$

$a_{11}x_{1} + a_{12}x_{2} + \dots + a_{1n}x_{n} = b_{1}$
$a_{21}x_{1} + a_{22}x_{2} + \dots + a_{2n}x_{n} = b_{2}$
$\vdots$
$a_{m1}x_{1} + a_{m2}x_{2} + \dots + a_{mn}x_{n} = b_{m}$

$A=\left( \begin{array}{ccc} a_{1,1} & \ldots & a_{1,n} \\ \vdots & \ddots & \vdots \\ a_{m,1} & \ldots & a_{m,n} \end{array} \right)$ , $\bar{x} = \left( \begin{array}{c} x_1 \\ \vdots \\ x_n \end{array} \right)$ , and $\bar{b}=\left( \begin{array}{c} b_1 \\ \vdots \\ b_n \end{array} \right)$

$\sum_{i=m}^n x_i = x_m + x_{m+1} + x_{m+2} +\cdots+ x_{n-1} + x_n.$

Practical example

$\sum_{k=2}^6 k^2 = 2^2+3^2+4^2+5^2+6^2 = 90.$

$\prod_{i=m}^{n} x_{i} := x_{m} \cdot x_{m+1} \cdot x_{m+2} \cdot \cdots \cdot x_{n-1} \cdot x_{n}.$

Practical example

$\prod_{i=2}^{6} \left(1 + {1\over i}\right) = \left(1 + {1\over 2}\right) \cdot \left(1 + {1\over 3}\right) \cdot \left(1 + {1\over 4}\right) \cdot \left(1 + {1\over 5}\right) \cdot \left(1 + {1\over 6}\right) = {7\over 2}.$

$\bar{x}=A^{-1}\bar{b}$

$det(A)\neq 0$

$m = n$

$d e t (A) = 0$

$m > n$

Examples of linear equation systems
$x + 5 y = 8$	$x 1 + 2 x 2 - 3 x 3 = 14$
$s = 1 / 2 x + 3 t - 1$
Examples of nonlinear equation systems
$x + y 2 = 0$	$a_{1}x_{1} + a_{2}x_{2} + \dots + a_{n}x_{n} = 1$
$s - sin t = 0$	$\sqrt{x} + 3y + 9z = 2$

[edit] More examples

$x + 2y = 10,\,$

$3a + 472b = 10b + 37,\,$

$2x + y -5 = -7x + 4y +3.\,$

$Ax + By + C = 0,\,$

$y - k = \frac{q - k}{p - h} (x - h),$

$y \sin \phi + x \cos \phi - p = 0,\,$

$a_1 x_1 + a_2 x_2 + \cdots + a_n x_n = b.$

$x = \frac{\sqrt{4ac+b^2}-b}{2a}$

$\left|x+\frac{b}{2a}\right| = \frac{\sqrt{b^2-4ac\ }}{|2a|}\Rightarrow x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac\ }}{2a}.$

[edit] Matrix example

$A = \begin{bmatrix} 9 & 8 & 6 \\ 1 & 2 & 7 \\ 4 & 9 & 2 \\ 6 & 0 & 5 \end{bmatrix}$ or $A = \begin{pmatrix} 9 & 8 & 6 \\ 1 & 2 & 7 \\ 4 & 9 & 2 \\ 6 & 0 & 5 \end{pmatrix}$

Math Examples

From FUKTwiki

[edit] More examples

[edit] Matrix example

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