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This is what I already have, but for the moment. In the left corner and the right corner there are two little vertical lines, I don't want them, but I don't know how to delete them. Anyone who can help me please?

\documentclass{standalone}
\usepackage[utf8]{inputenc}
\usepackage[math]{iwona}
\usepackage{eurosym}
\begin{document}
    \begin{tabular}{|c l l r|}
          & \huge{\textsterling} & \Large{\EUR{}} & \$ \\ \hline
        \textsterling & 10 & 8,9 & 6,2 \\ \hline \hline
        \EUR{} & 11,3 & 10 & 7,0 \\ \hline \hline
        \$ & 16,2 & 14,3 & 10 \\ \hline
    \end{tabular}
\end{document}

Example

This is what I need to become. So it are just the two little lines in each corner that I need to delete. But I don't know how :(

And as you can see, I really need the horizontal lines, because it is an exercise...

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Welcome to TeX.sx! Please add a minimal working example (MWE) that illustrates your problem. It will be much easier for us to reproduce your situation and find out what the issue is when we see compilable code, starting with \documentclass{...} and ending with \end{document}. –  Martin Schröder Jan 3 '13 at 9:50
2  
Can you provide an image of what you've got? I can't understand what problem you faced. –  m0nhawk Jan 3 '13 at 9:52
    
Your specification of the format for tabluar contains | at the beginning and the end, this causes LaTeX to print vertical bars at the beginning and end of each ordinary row. Are these the lines you are unhappy with? If so, just write \begin{tabular}{cllr}. –  Andrew Swann Jan 3 '13 at 10:07
    
Welcome to TeX.sx! Please always use specific titles which tell something about the specific problem. Imagine if we would have dozens of questions titled with "tabular problem" or similar, all about different problems with tabulars. Questions texts should also always start with text, not with code, so they are better displayed on the summary pages. To indicate which answer solved your problem (best) mark it as accepted by clicking the tick mark at he top left of the question. This concludes the question and assigns points to the answerer. –  Martin Scharrer Jan 3 '13 at 11:59
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2 Answers

You can overwrite the vertical rule spec via \multicolumn. Still the result is not very satisfactory and you might choose a different strategy via boxing the contents e.g. see Highlight a table row with a rectangular overlay etc.

\documentclass[border=3mm]{standalone}
\usepackage{eurosym}
\begin{document}
    \begin{tabular}{|c l l r|}
        \multicolumn{1}{c}{} & \huge{\textsterling} & \Large{\EUR{}} & \multicolumn{1}{c}{\huge \$}\\\hline
        \textsterling        & 10                   & 8,9            & 6,2\\ \hline \hline
        \EUR{}               & 11,3                 & 10             & 7,0\\ \hline \hline
        \$                   & 16,2                 & 14,3           & 10 \\ \hline
    \end{tabular}
\end{document}

enter image description here

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As the edited question show now that the problem is highlight the row with boxes and not delete completely vertical rules, this made my anterior answer obsolete.

Since percusse solution is perfect, just for fun this is a light variation that allow more flexibility, as you can box only selected rows (or cells or groups of cells changing \hline by \cline) as well as highlight also rows or cells with colors.

MWE

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\usepackage[utf8]{inputenc}
\usepackage[math]{iwona}
\usepackage{eurosym}
\usepackage[table]{xcolor}
\definecolor{lgray}{RGB}{230,230,230}
%\usepackage{array}
\begin{document}
\begin{tabular}{c l l r}
  & \huge{\textsterling} & \Large{\EUR{}} & \$ \\ \hline
\rowcolor{lgray}
\multicolumn{1}{|c}{\textsterling} & 10 & 8,9 & 
\multicolumn{1}{c|}{6,2}
\\ \hline  
\textyen & 11,5 & 9,3 & 4,2 \\ \hline
\multicolumn{1}{|c}{\EUR{}} & 11,3 & 10 & 
\multicolumn{1}{c|}{7,0} 
\\ \hline \hline 
\multicolumn{1}{|c}{\$} & 16,2 & \cellcolor{yellow}14,3 & 
\multicolumn{1}{c|}{10} \\ \hline
\end{tabular}
\end{document}
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Please avoid "Edit" markers in posts. Simply simply update the existing text to reflect the latest solution. Older versions can always be seen in the revision history, e.g. tex.stackexchange.com/posts/89049/revisions –  Martin Scharrer Jan 3 '13 at 12:00
    
@MartinScharrer, You are right, I deleted original answer. –  Fran Jan 3 '13 at 12:17
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