In Shakespeare's Hamlet, to what extent is Gertrude guilty? Was she "in on" her husband's murder?

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Information about Hamlet's father's death is acquired in Act I, scene iv, as the Ghost explains how he was killed. The Ghost says, "But know, thou noble youth,/The serpent that did sting thy father's life/
Now wears his crown" (I.iv.43-45). Here he explicitly reveals Claudius's role in the murder, but he does not say that Gertrude was in on it. The Ghost does say that Claudius is an "incenstuous. . . adulterous beast" (I.iv.47), which would link Gertrude to Claudius in some way, but the language is too ambiguous to conclude that Gertrude was in on the murder. The Ghost continues and explains that it was Claudius who put the poison in his ear while he was sleeping in the orchard, not Gertrude. He even pleads for Hamlet not to take revenge on his mother and let her be dealt with in Heaven. But the goal of revenge is to send Claudius to hell, which is another reason Hamlet doesn't kill him when he's praying in the chapel later. From what can be inferred from the text, Gertrude was more than likely seduced before the Ghost's death, but that doesn't necessarily mean that she was in on the murderous act. Again, the fact that the Ghost doesn't want to get Gertrude involved shows that he wasn't convinced that she was "in on" the murder. The fact that Gertrude marries Claudius very quickly after the King's death, though, does suggest that she wasn't altogether innocent of adultery before the murder.