DataTable with dynamic columns

I am completely new to JSF, and just attempting a proof of concept to decide whether it will be useful for a project. My POC simply consists of a single page, with a table, containing some data.

The number of columns (as well as the number of rows) is dynamic, loaded from a database before the page is rendered.

With the following, I get two static columns with the appropriate number of rows, as I'd expect:

<h:dataTable id="data" value="#{viewDataBean.dataRows}" var="row">
    <h:column>
        <f:facet name="header">
            <h:outputText value="Col 1"/>
        </f:facet>
        <h:outputText value="#{row.values[0].value}"/>
    </h:column>
    <h:column>
        <f:facet name="header">
            <h:outputText value="Col 2"/>
        </f:facet>
        <h:outputText value="#{row.values[1].value}"/>
    </h:column>
</h:dataTable>

What I wanted to do was to add a <c:forEach...> around a single set of <h:column>...</h:column> tags, to iterate over the number of columns, but that didn't work - I tried a variety of combinations, but I was expecting something like this to work:

<h:dataTable id="data" value="#{viewDataBean.dataRows}" var="row">
    <c:forEach items="#{row.values}" var="val">
        <h:column>
            <f:facet name="header">
                <h:outputText value="Col 1"/>
            </f:facet>
            <h:outputText value="#{val.value}"/>
        </h:column>
    </c:forEach>
</h:dataTable>

From Googling, I've read various vague comments like 'that's not the way to do it', but I haven't been able to find any particularly compelling examples of the right way. Someone mentioned building the DataTable in the backing bean, but the only example of that I could find was