I've been looking around and I can find plenty of tutorials and videos, but I find that the best way to learn something is by working through practise problems. Even better when there are solutions.
Something like projecteuler.net is good, but I need something which is more specific to MATLAB and will allow me to master all the basics of MATLAB
You're right that there aren't a whole lot of problem and solution sets, but here's a page of some problems to get started with: http://www.facstaff.bucknell.edu/maneval/help211/exercises.html
Also, if you simply go to Help -> Demos in Matlab, there are videos available which you can follow along with and learn all the basics.
Lastly, this isn't Matlab-specific, but if you're interested in digital signal processing, check out DSPguide.com. It is a free book online which covers all the basics of DSP, and just about everything discussed (filters, transforms, etc.) has Matlab built-in functions, so you can look up the functions and learn how to do DSP while you read along with the eBook. No problems and solutions in the eBook, but you'll still learn the Matlab functions and how to use them as you read along.