Math 215 HW #9 Solutions

Another way to get an upper bound is to use the big formula for the determinant from p. 212. Notice that, for any 5 by 5 matrix, there are 5! = 120 terms in the sum. When all entries of A are smaller than 1 (in absolute value), it must be the case that each of the 120 terms in the sum is smaller than 1 (in absolute value). Therefore, the whole sum (which is just the determinant), must be no bigger than 120 in absolute value.