Why does Hamlet kill Polonius through the arras even though he passed Claudius praying?

Whenis
summoned by his mother he doesn't know
whether she had any involvement in his father's murder.
She might have been
an accessory before the fact or after the fact or completely ignorant of

whatwas going to do or what he had done after it was done. She has good cause to think
her son
is insane. He knows he is not insane. He has also assured himself
(and the audience) that he
intends no harm to her. In Act 3, Scene 1, he
tells himself:

Now to my mother. />O heart, lose not thy nature. Let not ever
The soul
of Nero
enter this firm bosom.
Let me be cruel, not unnatural.
I
will
speak...

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