Adjusting extent of raster using ArcGIS Desktop?

The coloured file contains landuse information and it needs to have the same number of columns and rows as the DEM in the background for further processing. I can't get it to work - "clip" and "extract by mask" haven't generated the results I need.

It's supposed to keep its values within the coloured areas - but outside of that to the borders of the DEM (the whole black and white area) I need it to have NoData values.

Use the raster calculator, set output extent and snap raster to the DEM in the tool environment, then use the land use raster layer as the expression. Easiest way to do that is to double click the land use raster layer in the layer list.

The output will be a raster with the extent of the DEM with NoData where there are no the land use values.

You can do this using the Raster Clip tool. You need to use the polygon dataset for the "Output Extent" parameter and then make sure that "Use Input Features for Clipping Geometry" is selected. This will fill the output dataset with the value you set for "NoData Value" for ever cell that is outside of the polygon boundaries.