Lady Macbeth plans the whole from start to end and she is presented as a cold-hearted evil person but why doesn't she actually commit Duncan's Murder, why does she manipulates Macbeth to kill Duncan if she has the capacity to commit murder

http://www.sparknotes.com/shakespeare/macbeth

Look particularly at the Character analysis section.

Lady Macbeth, in Shakespeare's play "Macbeth," indeed plays a significant role in plotting the murder of King Duncan. While she is portrayed as a ruthless, ambitious character, she does not personally commit the act herself for a few reasons:

1. Socio-Cultural Factors: In the Jacobean era, when the play was written, women were generally regarded as subordinate to men, and it was considered socially unacceptable for a woman to commit such a heinous act. Lady Macbeth recognizes this societal expectation and manipulates Macbeth into taking action, considering that he, as a man, would be more easily accepted and less scrutinized for it.

2. Psychological Factors: Lady Macbeth possesses the desire for power but lacks the necessary capacity to carry out the murder herself due to her own psychological limitations. Throughout the play, she reveals moments of vulnerability and moral conflict, as evidenced by her sleepwalking and guilt-ridden soliloquies.

By manipulating Macbeth, Lady Macbeth relies on his ambition and masculinity to convince him to commit the murder. She challenges his manhood, questions his courage, and plays upon his ambitions, ultimately appealing to his sense of power and greatness. By using psychological tactics, she overcomes her own limitations and convinces Macbeth to become the instrument of her ambitions.

Understanding Lady Macbeth's role as a manipulator rather than an executor of the murder enhances the complexity of her character and the layers of the play's exploration of ambition, guilt, and gender expectations.