Welcome to genvibe!
Which wire harness are you asking about? If its the radio, then that would be fairly straightforward. If its the engine, well, that's awful. Hope its just the radio
If its the radio, then check out the 04 Toyota Matrix wiring diagrams at
https://cardiagn.com/2004-07-toyota-cor ... m-em0350u/ Should be the same as for your 03 Vibe. (wire color "L" = blue) If you load the Overall wiring diagram from that site, the radio wiring is on pages 39 and 40, depending on what audio set up the car came with. I prefer the "System Circuits" PDF, easier to read and wires are shown in their colors, if you use that one, the audio stuff starts at page 140 of the PDF.
If you load that wiring diagram, save to to a local storage. Could come in handy later
If you have a sunroof and tweeters in the door, then you should also have a separate audio amplifier under the front driver seat. If you don't have a sunroof, then no external amplifier.
Unless, of course, the previous owner did some weird stuff with a prior aftermarket audio install.
On the Metra harness, those are potentially different for different aftermarket radios. Are you trying to install an aftermarket radio, or are you trying to install an OEM radio after the factory harness was cut out?