Might be more interesting if we replace the permutation matrix with an arbitrary 5 x 5 matrix over the reals.
Which of these expressions do you think will be the largest?
1. a[1,1]*(number of people choosing 1) + … + a[1,5]*(number of people choosing 5)
...
5. a[5,1]*(number of people choosing 1) + … + a[5,5]*(number of people choosing 5)
Might be more interesting if we replace the permutation matrix with an arbitrary 5 x 5 matrix over the reals.
Which of these expressions do you think will be the largest?
1. a[1,1]*(number of people choosing 1) + … + a[1,5]*(number of people choosing 5)
...
5. a[5,1]*(number of people choosing 1) + … + a[5,5]*(number of people choosing 5)