To find out how much money Gemma had left in her checking account after she wrote the check, you need to subtract the amount of the check from her initial balance.
Initial balance: $2,054
Amount of the check: $584
Now, performing the subtraction:
\[ 2,054 - 584 = 1,470 \]
Therefore, after the landlord cashed the check, Gemma had $1,470 left in her checking account.