What was the first song Dave Matthews wrote, and for whom was it written?

The first song Dave Matthews ever wrote was 'I'll Back You Up.'

Dedicated to Matthews' girlfriend at the time, Julia Grey, this was the first song Dave Matthews wrote.

https://www.songfacts.com/facts/dave-matthews-band/ill-back-you-up

Many believe that 'The Song that Jane Likes' was the first song written by Dave Matthews. This is a false statement because 'TSTJL' was the first song with music completed. 'I'll Back You Up' was the first song with lyrics completed. This song was written for a girl that Dave Matthews was going out with, he cared very deeply for her, and wrote this song for her. He asked her to marry him three times, however she turned him down all three times. He later on wrote the song 'Halloween' to express his feelings of hatred towards her.