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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="rref">
    <refnamediv>
        <refname>rref</refname>
        <refpurpose>computes  matrix row echelon form by lu transformations</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>R=rref(A)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para> m x n matrix with scalar entries</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>R</term>
                <listitem>
                    <para> m x n matrix,row echelon form of a</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>rref</literal> computes the row echelon form of the given matrix by left lu
            decomposition. If ones need the transformation used just call
            <literal>X=rref([A,eye(m,m)])</literal> the row echelon form <literal>R</literal> is <literal>X(:,1:n)</literal> and
            the left transformation <literal>L</literal> is given by <literal>X(:,n+1:n+m)</literal> such as <literal>L*A=R</literal>
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=[1 2;3 4;5 6];
X=rref([A,eye(3,3)]);
R=X(:,1:2)
L=X(:,3:5);L*A
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="lu">lu</link>
            </member>
            <member>
                <link linkend="qr">qr</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
