问题补充：
they are determined to carry out the plan,
答案：
no matter what 只能引导状语从句,如：No matter what happened,I would not agree.
whatever不仅可以引导状语从句,也可引导名词性从句.
引导状语从句时,两者可互相转换.但引导名词性从句时,只能用whatever
本题显然是引导的名词性从句,whatever difficults,“不论什么样的困难”意思=no matter what difficults,但是在句子里只能用whatever
