I like to compare a UTXO to a fiat "note" but without defined denominations. If you want to pay someone, you need to gather up enough notes (inputs) to pay (outputs) plus fee (mining). Usually, you'll have sats left, so you'll need another note paid to yourself (change output).
Also, each input in the tx needs it's own signature/script in order to be spent.
Hm, I've got all that covered except for the mining fees + change output, but I knew about that already, sharp.
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Each transaction is signed…
This is not semantically correct. My 2nd point is that each input needs their own signatures for a tx to be valid.
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Because each transaction can consist of multiple UTXO's, which each have to be signed, gotcha.