The head of household shall be eligible for a reduction computed pursuant to the schedule in § 10-6B-7 if each of the following conditions is satisfied:
(1) The head of household is a widow or widower;
(2) The dwelling upon which the reduction is claimed qualified for and received a reduction pursuant to § 10-6B-7 in the year immediately preceding the death of the deceased spouse;
(3) The head of household has continued to live in the same dwelling;
(4) The head of household has not remarried.