How to get better at row reduction?

[Noone1982]

Please don't say just practice. Any specific tips?

In my class we're not allowed to use calculators, consequently I am spending all my time row reducing to find basis, dependence, etc. Frankly, I am just horrible at it, I just can't see how to get to the end.

I am a bit perplexed on the no-calculator-policy. I mean, sure doing things by hand is great, but it detracts us with the unending arithmetic. What is your view on it?

 

[TD]

Row reducing isn't hard, it's just annoying. It doesn't involve any kind of mathematics which you could consider as 'hard', it's simple arithmetic.

Try to be systematic in your way of row-reducing and be careful everytime you calculate a new element, double-check your arithmetic. This takes a bit longer but it saves you a load of time compared to finding errors somewhere along the way.

 

[shmoe]

If you don't already you might want to use some kind of shorthand notation to keep track of your steps. In the event of an error, it can make checking your work easier. e.g. if from one step to the next you've added 2 times row one to row two you could write R_2\rightarrow R_2+2R_1.

It's simpler to ban all calculators as some can do all of this computational stuff you'll see with matrices for you. Hopefully you aren't graded too harshly on a few arithmetic mistakes though, that you understand the process involved is much more important in my opinion.

 

[tmc]

theyve never allowed us calculators in algebra. Would seem like a waste of time anyways.

 

[mathwonk]

you are not asking for advice, just sympathy. or as harry truman put it when someone said he always seemed to know what should be done: "everyone knows what should be done, they just don't want to do it."

 

[quantumdude]

Please don't say just practice. Any specific tips?

Yes: Practice.

 

[Galileo]

Practice with it. Screw up a lot.
Practice more. Screw up again.
Practice more. Screw up less.
Practice some more. Screw up occasionally.
Practice more again. Hardly screw up anymore.

You get the idea

 

[FrogPad]

Noone1982 I felt your pain when I was taking linear algebra. Especially since I was a computer science student (I just changed my major). I was like: "all of this could just be reduced to a program on a computer. Why am I even learning this?"

When I was first in the class, I was doing all my homework on my calculator. Then, on the first test there was a 6x6 determinant. It was taking me FOREVER to do the problem. So, I moved onto the next problem. Finding the inverse of some matrix (I think it was a 3x3) which isn't too bad. But anyhow... again, it took me forever. Needless to say, I screwed up BAD on my first exam. So after that I just got over my whining about not having a calculator, and just put the damn thing away to do all my homework. I didn't get less then a 95 on the rest of my exams, and I can add/subtract/multiply much much faster because of that. It's pretty amazing how dependent you can get on those little machines. Also the more you just practice, the better you become at it BECAUSE of the fact that you learn little notational "tricks" to do the problem. You find out that you will constantly get the wrong answer because you are not being systematic, and you relaize you have to just relax and take it step by step. (At least it did for me). So a tip that made me somewhat (not amazing or anything) proficient at it is: make mistakes.

 

[mathwonk]

and think about what you are doing and how it is proceeding while you are practicing. the idea is not so much to become skillful at mindless calculation but to gain insight into the nature of the process.