In lines 40-41 Matthew Arnold states that the middle class of 19th century England were like Philistines, obsessed with respectability.
So in going through the answer choices, we do not see one that clearly states that they became patrons of the arts in order to earn respect. So we must examine the answer choices a little bit closer.
A) Arnold did not say that believed in the importance of art.
B) Nor did he say that they sponsored art to have something other than that from commissioned by the aristocracy.
C) Arnold did not link the middle class with a desire to make money through art.
D) Arnold did not say that they were concerned with creating high quality art.
E) The only answer choice that is not immediately incorrect. We can reasonable conclude that establishing a reputation as a patron of the arts is akin to earning social respect. This coincides with Matthew Arnold's characterization of 19th century English middle class' involvement in sponsoring art.
I hope this helps. Please let me know if you have any other questions.