When Germany attacked the Lusitania during WWI, why did they do it and did they know it was an American ship?

At first Germany respected neutral shipping and penger liners,but it was soon clear that their U-boat blockade was not effective.This was partly because they had insufficient U-boats and partly because there were problems of identification:the British tried to fool the Germans by flying neutral flags and using penger liners to transport arms and ammunitions.In April 1915 the British liner Lusitania was sunk by a torpedo attack.In fact the Lusitania was armed and carrying vast quantities of arms and ammunitions, as the Germans knew;hence their claim that the sinking was not just an act of barbarism against defenceless civilians.