SAT® writing question: When to use the "having" phrase?

[Chelsea]

Why is this sentence incorrect?

9. Having command of pathos, tragedy, as well as humor, George Eliot is considered to be a great English novelist.

a) Having command of pathos, tragedy, as well as humor
b)Having command of pathos, tragedy, and her humorous side
c)By being in command of both pathos and tragedy and also humor
d)With her command of pathos and tragedy and being humorous
e)Because of her command of pathos, tragedy, and humor

I see why e is the better choice, but I don't know why a is incorrect. When do you use the "having" phrase?

[Mister Micawber]

Because the subject of a nonfinite clause must be the same as the agent of the main clause. There is also a structural problem within the first clause. This would be OK:

Having command of pathos and tragedy, as well as humor, George Eliot is a great English novelist.
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Native English teacher at Mister Micawber's