XSLT : Add a namespace declaration to the root ele

I have this XML document :

<?xml version="1.0" encoding="utf-8"?>
<Wix xmlns="http://schemas.microsoft.com/wix/2006/wi">
    <Fragment>
        <DirectoryRef Id="AcquisitionFolder">
            <Directory Id="dir2EE87E668A6861A2C8B6528214144568" Name="bin" />
            <Directory Id="dir99C9EB95694B90A2CD31AD7E2F4BF7F6" Name="Decoders" />
        </DirectoryRef>
    </Fragment>
</Wix>

I'd like to obtain the following result :

<?xml version="1.0" encoding="utf-8"?>
<Wix xmlns="http://schemas.microsoft.com/wix/2006/wi" xmlns:util="http://schemas.microsoft.com/wix/UtilExtension>
    <Fragment>
        <DirectoryRef Id="AcquisitionFolder">
            <Directory Id="dir2EE87E668A6861A2C8B6528214144568" Name="bin" />
            <Directory Id="dir99C9EB95694B90A2CD31AD7E2F4BF7F6" Name="Decoders" />
        </DirectoryRef>
    </Fragment>
</Wix>

It seems a simple problem, but I didn't find the solution :-( I made several attempts, and found several similar questions (this one for example : XSLT: Add namespace to root element), but they didn't help me.

Thanks for any advice !!!

In many cases, you can simply embed the namespace into the projected Xml elements (including root) as part of a Literal Result Element:

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet 
    xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
    version="1.0">
    <xsl:output method="xml" indent="yes"/>

    <xsl:template match="/*[local-name()='Wix']">
        <Wix xmlns="http://schemas.microsoft.com/wix/2006/wi"
             xmlns:util="http://schemas.microsoft.com/wix/UtilExtension">
            <xsl:copy-of select="node()|@*"/>
        </Wix>
     </xsl:template>
</xsl:stylesheet>

More formally / generally, any namespaces in your output xml can be added into the stylesheet's own declaration (either globally, or using a namespace alias), e.g.

<xsl:stylesheet 
    xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
    xmlns:wix="http://www.foo.com/2001/v1"
    ...other namespaces here>

... and then referenced in the output

<xsl:template match="/">
    <wix:Wix>
       <wix:Child>
          ...

If there are unwanted / unused namespaces residual in the resultant output (e.g. needed in the source document, but not in the output document), you are able able to clean these out with exclude-result-prefixes