I have another question for my homework and i have been looking all week and it is due tomorrow.I have been looking and cant find an exact answer and i dont want to give the wrong answer on my homework. my ist question is where is the kernal executable program stored in the Linux directory hierarchy and what is the file name of the Linux kernal stored in that directory? my second question is mored or less just seeing if i am right. the question is how would you allow s user to execute privileged commands without giving the user the superuser password? I am pretty sure that you would use the su command with the -c option to run a single command with root privileges, and then once it is finished the user would go back to the original shell. correct?

The kernel can be stored at any random position, as long as the bootloader can see it. But usually they are stored at /boot, it can have any name as well. Traditionally "vmlinuz" is used. For more info you should read about lilo and grub and how they are configured. Also, google for manuals to compile and install a custom kernel. Covering these two topics you should end with a clearer view of the whole thing.

Yes. Read also about "sudo" and "suid".