How does Shakespeare's presentation of the female characters in Hamlet further his purposes?

Gertrude and Ophelia are presented as weak women subject
to the various actions of men. Throughout the drama they react, rather than act with
resolve or firm moral determination. Ophelia's suicide might seem to be an action born
of determination, but it is really a reaction to all she has endured in her
male-dominated young life.

These female characters in their
weakness serve several purposes in the play. First, through them the plot is advanced.
Gertrude's seduction by Claudius sickens and infuriates Hamlet, further pushing him into
avenging his father's murder. Through his relationship with Ophelia, the daughter of
Polonius, Hamlet plants the first seeds to suggest that he has gone mad, an integral
part of his plan to discover the truth about his father's death. Additionally, it is
Ophelia's death that drives Laertes into the plot with Claudius to kill
Hamlet.

Also, in his relationships with these two weak
women, Hamlet's complex character is more deeply developed. He is appalled by his
mother's behavior, but he loves her and tries to save her from further acts of
debasement; his relationship with her intensifies his torment. His relationship with
Ophelia further torments him. He uses Ophelia in his plot against Claudius, but in doing
so, he deliberately pushes her away while loving her deeply. Ophelia's death causes
Hamlet great agony.

Gertrude and Ophelia are important in
the drama not for the women they are but for the passive roles they play in Hamlet's
tragic destruction.