Originally, 을 수 없다 is a short form of "을 수가 없다" If you use 을 수가 없다, you can emphasize your feeling. Here are some variations. 을 수도 없다. I can't do something neither 을 수는 없다. I can't do something, but... 을 수 조차 없다. even I can't do something 을 수 밖에 없다. only I can't do something

It does still mean the same thing. 가 is used additionally. As you might know, when you're talking about a subject using 있다/없다 you can add (or not) the subject marker 이/가. e.g. 시험 있다/시험이 없다. Either the way, the message is understood in the same way. Because this grammar you are learning now contains 있다/없다, you can add or not 이/가 before the verb. I hope it helps..