Based on what you've seen in Act 3, Scene 4 of Hamlet, do you think Gertrude knew about the murder?
The text suggests that Gertrude has no idea what Hamlet is referring to when he talks about the murder of a king. Hamlet is confrontational and rude from the outset of their conversation. His mother is shocked by his harsh tone and fears for her life. When it seems as if Hamlet is going to assault her, she cries out. Her desperate cry leads to Polonius (who is hiding behind the arras) also crying out. Hamlet stabs him through the arras, killing him.
When Gertrude cries out that Hamlet has committed "a most rash and bloody deed," he compares what he has just done to the act of killing a king and marrying his brother. He alludes to what his father's ghost had told him about its own demise when it stated that Claudius poisoned it and then married Gertrude and assumed the throne. Hamlet says:
A bloody deed! almost as bad, good mother,
As kill a king, and marry with his brother.
Gertrude's shocked response indicates that she does not know what Hamlet is talking about:
As kill a king!
Her question emphasizes her lack of knowledge:
What have I done, that thou darest wag thy tongue
In noise so rude against me?
Hamlet's overly dramatic and metaphoric reply confuses her even more and she seeks further information:
Ay me, what act,
That roars so loud, and thunders in the index?
Hamlet verbally lashes out at his mother and severely reprimands her for having married one so unworthy of filling his father's shoes. He rants about the fact that she could not have been driven by love and says that she should be ashamed of what she has done for she was driven by lust.
Gertrude is, of course, aghast at Hamlet's assertions and seems to realize how much grief she has brought him. She asks him to stop speaking and acknowledges some guilt.
O Hamlet, speak no more:
Thou turn'st mine eyes into my very soul;
And there I see such black and grained spots
As will not leave their tinct.
Hamlet is relentless, however, and uses foul and lewd descriptions of his mother's deeds. Gertrude is overwhelmed by her son's damning tirade and begs him to stop. It is only when the ghost intervenes and tells him to comfort his mother that Hamlet softens somewhat. When he beseeches her to confess her sins, Gertrude tells him that he has broken her heart with his claims.
Hamlet later employs a different approach. He asks her to first refuse to sleep with Claudius for a few nights. She should then, when he cannot tolerate her absence any longer, woo him and convince him that he (Hamlet) is not mad, but crafty. Gertrude responds by telling him that she would be incapable of uttering a word of what her son has told her.
It is ironic later when Gertrude speaks to Claudius and he asks about her son's condition that she tells him:
Mad as the sea and wind...
The fact that Gertrude was so distraught and overcome by Hamlet's assertions makes one believe that she has no knowledge of what Claudius has done. She gives no inkling that she was involved in any way--either directly or indirectly.
If you are referring to the murder of Hamlet Sr., it is certainly not stated explicitly that she knew anything about it or even suspected it. Hamlet makes some reference to it, calling Claudius a murderer but does not go into it further. Of course, Gertrude doesn't call him on this either so perhaps she is in some ways indicating that she understands Hamlet's feelings about it?
When Hamlet refers to Claudius as "A murderer and a villain, A slave that is not twentieth part the tithe of your precent Lord," Gertrude says only "No more." but it would be difficult to construe this as an indication that she was aware of Hamlet Sr.'s murder.