Final answer:
Grigori Rasputin had considerable influence over the Russian Royal Family due to his perceived ability to heal the heir to the throne, Alexei, and Tsarina Alexandra's belief in his divine appointment.
Step-by-step explanation:
Rasputin held a significant influence over the Royal Family due to his ability to alleviate the symptoms of hemophilia in Tsar Nicholas II's son, Alexei. Tthe Tsarina Alexandra heavily relied on his advice, believing him to be sent by God, thus allowing him considerable sway over the monarchy's decisions. This reliance became particularly evident when Nicholas II left to command the army in World War I, leaving Alexandra and Rasputin to make unpopular decisions that eroded public support for the monarchy. Meanwhile, Prime Minister Stolypin, along with other members of the aristocracy, viewed Rasputin's influence and the ongoing corruption as damaging to Russia, resulting in a conspiracy that ultimately led to Rasputin's assassination. Though detailed records of Stolypin's explicit intentions towards Rasputin are not mentioned, it is reasonable to infer based on the political context that Stolypin, along with other political figures, desired to see Rasputin removed from his position to restore stability and diminish the monarchy's declining reputation. The situation was exacerbated by Tsar Nicholas II's reluctance to limit his absolute power, despite the vast ethnic, linguistic, and religious diversity of the Russian Empire which created administrative complexities. Moreover, Rasputin's behavior and rumors surrounding his personal life sparked further discontent among the public and nobility alike.