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Update README.md

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Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
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@ -29,7 +29,7 @@ A major advantage of Matlab in comparison to a conventional programming language
| | | | | | | |
| ------------- |:-------------:|:-------------:| | ------------- |:-------------:|:-------------:|
| `a = [3;1];` | defines a column vector | $\vec{a} = \left(\begin{array}{c}3\\1\\\end{array}\right)$ | | `a = [3;1];` | defines a column vector | $\vec{a} = \left(\begin{array}{c}3 & 1 \end{array}\right)$ |
| `a(k)` | means the vector component | $a_k$ | | `a(k)` | means the vector component | $a_k$ |
| `b = [0,3,-4];` | defines a row vector | $\vec{b} = (0,3,-4)$ | | `b = [0,3,-4];` | defines a row vector | $\vec{b} = (0,3,-4)$ |
@ -43,29 +43,29 @@ $3x+y = 1 $
can be formulated elegantly: can be formulated elegantly:
$$ \left(\begin{array}{cc} 1 & 2 \\\\ 3 & 1 \\ \end{array}\right) \left(\begin{array}{c} x & y \\\\ \end{array}\right) = \left(\begin{array}{c} 3 & 1 \\\\ \end{array}\right) $$ $$ \left(\begin{array}{cc} 1 & 2 \\ 3 & 1 \end{array}\right) \left(\begin{array}{c} x & y \end{array}\right) = \left(\begin{array}{c} 3 & 1 \end{array}\right) $$
respectively respectively
$D\,\vec{x} = \vec{b} $ $$D\,\vec{x} = \vec{b} $$
with the $2\times 2$ matrix with the $2\times 2$ matrix
$ D = \left(\begin{array}{cc}1 & 2\\3 & 1\\\end{array}\right) \begin{array}{c}\leftarrow\;\;\mbox{1. line}\\\leftarrow\;\;\mbox{2. line}\\\end{array}$ $$ D = \left(\begin{array}{cc}1 & 2 \\ 3 & 1 \end{array}\right) \begin{array}{c}\leftarrow\;\;\mbox{1. line} \\ \leftarrow\;\;\mbox{2. line} \\ \end{array}$$
$\nearrow$ $\nwarrow$ $$\nearrow \nwarrow$$
1. line 2. line 1. line 2. line
and the column vectors and the column vectors
$ \vec{x} = \left(\begin{array}{c}x\\y\\\end{array}\right) \quad\mbox{and}\quad \vec{b} = \left(\begin{array}{c}3\\ 1\\\end{array}\right) $. $$ \vec{x} = \left(\begin{array}{c}x & y \end{array}\right) \quad\mbox{and}\quad \vec{b} = \left(\begin{array}{c}3 & 1 \end{array}\right) $$
Here, $\vec{x}$ is the solution vector being sought. Here, $\vec{x}$ is the solution vector being sought.
The formal solution of the equation $D\,\vec{x} = \vec{b}$ is given by The formal solution of the equation $D\,\vec{x} = \vec{b}$ is given by
$\vec{x} = D^{-1}\, \vec{b} \, ,$ &$\vec{x} = D^{-1}\, \vec{b} \, ,$&
where $D^{-1}$ denotes the inverse of the matrix $D$. where $D^{-1}$ denotes the inverse of the matrix $D$.