Tutoring is depressing because my students are struggling too much with my exercises. What do I do? I am a tutor for first year students in mathematics, and I feel pretty bad about it.

I recently changed universities. At my previous university, where I also tutored, the exercises were very demanding for the students; the problems were interesting and not easy. So I was really glad to be able to help.

Now, this is not the case anymore. Exercises consist simply of paraphrasing the definitions, and almost all the students are struggling pretty hard on these very simple exercises. Typically, they think that solving Ax = 0 when A is a 3×3 matrix is too hard. They have very little intuition about what is going on, especially in algebra. When they ask me questions, I try to answer so they see a way of thinking that can be generalized. But sometimes they just look at me as if I was an alien.

I am not here to complain, but to ask for advice. What should I do? Should I simply answer their questions as simply as possible? What I really want is to push them to work harder and become more familiar with mathematics. On the other hand, I am probably doing this already a bit and I don't want them to be disgusted by mathematics. I really don't know what to do. 

Edit: Thanks everyone for your answers and your comments! This is really helpful. As asked here is some more detail: I am a tutor for students in the first year of a university in Europe. We are two tutors, staying in a classroom during 3 hours and answering every question they ask to us. I am paid by university, this is not private tutoring. They are studying mathematics, so they are not e.g. engineers. (In fact, two years ago I did teach complex and Fourier analysis to engineers in my previous university and I was surprised by the high level of the class! They were only in second year but got very hardcore stuff to do, and some of them were doing very well!) My current university does not organize one tutoring session for each class but only one "big" session where we should answer questions on all subjects: geometry, algebra and calculus.
What you're experiencing is pretty much what all college teachers are wrestling with all the time everywhere. 

Allow me to point out that the abyss of need can go much, much deeper than what you're currently dealing with. In the U.S., most college students are attending a community college. And most students entering U.S. community colleges do not have 8th grade algebra skills, nor even 6th grade arithmetic skills (e.g., fractions, proportions, negatives, estimations, times tables). I've had a good chunk of a college math lecturer career at this point and I've never taught anything as high level as matrices. 

Here's how I've been able to jiu-jitsu it in my own mind. Think of it like a diagnostician. Doctors have to find it fascinating to track down hideous diseases. Detectives have to find it compelling to decipher ostensibly horrible crime cases. So too: I find it endlessly fascinating to diagnose what exactly is the block or problem in students' heads, or to track down the place where their reasoning first went off the rails. Ask questions to try and find where their reasoning starts and where it stops. Do something of a binary search to try to narrow down the problem spot. I'm continually discovering new gaps in people's knowledge that I never would have expected. It's surprising and amazing every day. 

Usually I do find that students simply cannot remember starting definitions. If they've come up through a system that depends on raw faith and memory (and not mathematical reasoning), they don't get how important that axiomatic basis is. Many also clearly have learning disabilities that make this difficult for them. "All your answers are back in the definitions", I say several dozen times per semester. Have the book handy so you can turn back to the starting definitions at any time, and see if they recall or can see how their reasoning got off track that way. In fact -- this explains why at your current school they're asking students to reiterate definitions; whereas for us that's natural and obvious, for some it's an overwhelmingly difficult blind spot to fill in.