How can I write a Linux Bash script that tells me which computers are ON in my LAN?
It would help if I could give it a range of IP addresses as input.
In the real world, you could use nmap to get what you want.
nmap -sn 10.1.1.1-255
This will ping all the addresses in the range 10.1.1.1 to 10.1.1.255 and let you know which ones answer.
Of course, if you in fact want to do this as a bash exercise, you could run ping for each address and parse the output, but that's a whole other story.