"The user is to input a number..."
How is the user providing these inputs? If you're using the input() function, don't. It's highly unconstrined allowing the user to enter virtually anything (more info: link1, link2).
"How do I correspond the user input A7 to a position on the plot, for example row=1, col=7?"
The numeric part already corresponds to the column number. To convert the letter A:Z to row numbers,
rowNumber = double(upper(char(letter)))-64
"how can I randomly determine a letter-number combo for the computer and correspond it to a row,col position"
M is the size of your matrix.
n is the number of random samples you want
randLetters = char(randi([65, size(M,1)+64],n,1))
randNumbers = randi([1,size(M,2)],n,1)
If you want to combine the letters and numbers, into the form 'A1', the numbers need to be converted to characters.
LN = strcat(randLetters, compose('%d',randNumbers))