There are no doubt a heap of applications to Computer Science by use of Linear Algebra, but as far as a regular undergrad degree goes you won't encounter a whole lot of it, or possibly none at all. As I said, Cryptographic techniques (in encryption) you can definitely find a use for it, and I guess in any sort of game major in terms of vectors.
I just don't want to people to think "There's heaps of maths in comp sci, I don't want to do it" because you pretty much don't need any maths for it. Maths certainly does help you in terms of logical thinking, but as far as applications go (and especially software applications in the real world in a general case) there won't be a lot of maths.
It depends where you're coming from though. You may be a whiz at maths, and consider MX1/MX2 HSC maths a no brainer. But for other people on these forums, they may be coming from backgrounds involving only limited maths, say 2 unit (advanced) or general maths or no senior year maths at all. For these people a Comp Sci would serve as a real shock, and would probably struggle doing a $400 2-week intensive maths bridging course if you had no prior senior maths experience or only did general maths.
Basically, if you've done at least Maths 2 unit (advanced) in the HSC, you should be able to jump the hoops of the $400 2-week bridging course at UNSW. Maybe a few general maths people would be able as well, but the morale/level of persistence drops as maths level drop. There's a reason why people get classed into several maths stream at high school. It prepares them for what it would take to do a 'logical and critical thinking course" at uni.
If you're like me and did 2 unit maths (advanced) back in school and barely managed to get that band 5. I suggest look elsewhere, but if you are really content and are willing at putting in extra hours for study (I'm talking weekends and holidays here, when all of your friends are having fun), then by all means do comp sci. One important quote to remember is "Put in the hard yards now, and the rewards will be greater later on".
Also note: Different unis require different maths levels for their comp sci courses:
UNSW (most intensive maths in comp sci): MX1 recommended, MX2 seen as a bonus. (There are about 3-4 Maths subjects studied in comp sci, 1st and 2nd year as far as I can remember, Software Engineering do 2 additional maths subjects, stats/probability and an additional maths subject).
UoW: Maths 2 unit (advanced) recommended.
USyd: MX1 recommended.
UTS (ICT Engineering-not comp sci, but it's the closest course UTS currently has): MX1 recommended.
I've had friends who did general maths in school and failed stats subjects for comp sci. I've also had general maths friends who have gone into engineering and done well. I guess it's up to you and whether or not you're a 'critical/pattern problem solving thinker'.
Check the course structure for each degree. That's what I did when applying for a course.
Hope that helps!