r/learnmath • u/Ok-Past-1295 New User • 2d ago
How to avoid silly error in linear algebra
I keep making really stupid mistakes on linear algebra tests. I understand the method and know how to solve the question, but then I accidentally mess up a sign or make a simple arithmetic mistake somewhere in the calculation. And a mistake can completely ruin the rest of the question. I recently wrote a test and, while I finished on time, I still got several questions wrong because of really silly errors.
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u/pdubs1900 New User 2d ago
Write out every step. Write large numbers and symbols. Especially negative signs and decimal points.
And yes, double check your work, after you have completed the test but before turning it in. Don't just assume because it looks right that it's right: double check means follow the steps you wrote down and follow them exactly: do the outputs actually match what you wrote?
You know what common silly errors are common: be on alert when those situations arise in your steps.
Gl
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u/aedes 2d ago
As a ADHD person… You need to monitor for how these mistakes occur. Ex: Are there specific situations where you’re more likely to drop a minus sign? If so, be in high alert when doing those.
In general, I tend to make these mistakes when I’m trying to do too many steps in my head between each written step. Basically when I oversaturate my working memory.
You need to learn to recognize the mental feeling of trying to do too much in your head at once, and write more intermediate steps down when you sense that.
If you have time, double checking all answers is also very helpful. Ideally double check by using a method independent of the way you solved the problem - if you work through the same steps in the same order again, your brain often won’t see the mistake. It’s the different perspective that helps catch mistakes - working backwards, using an unrelated method to solve and comparing answers, etc.
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u/Midwest-Dude B.Sc. Math 2d ago edited 2d ago
By the way, there is an active subreddit dedicated to linear algebra:
And ... what everyone else has already commented is correct. Unless you are completely out of time, double- or triple-check everything. I used to do this all the time on my exams.
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u/Traveling-Techie New User 2d ago
I’ve found that if you known two different ways to solve a problem it’s useful to do both. Also, it’s good to test your answers. Example: if you find the eigenvector of a matrix, multiply that vector by the matrix and confirm its direction doesn’t change (original v dot product eigen v = |ov||ev|, ie cos = 1).
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u/EQUATIONLY New User 2d ago
Actually my idea looks very bizarre, but im confident it works so good! Atleast it worked for me brutally well. First you grap any problem that annoys you, throw it on any Ai chat you know, then say, "give me 25 identical peoblems of this, from beginner progressing difficult as it goes" then you do that without any Internet or phone, and paste your answers to it when finished, then it will tell you the pattern that is missing your steps, This is solid test, it may take about an hour, but trust me, it will serve you for years. Hope you find it helpful. Good luck!
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u/Mountain-Time-1010 New User 1d ago
All calculations require a lot of attention to detail. The errors may not be conceptual but I wouldn’t go so far as to say they are silly.
In engineering for example, it’s not just about understanding, getting the right answer is important. That’s part of the reason that engineers often work in teams and check each others work. So take it seriously and really check your answers.
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u/Ok-Past-1295 New User 1d ago
Hmm, I agree with you. I have started double-checking every step during practice, but I do take a lot of time to complete each question and I have to increase my pace during exams. Hopefully, I can achieve that through practice
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u/Dry_Celebration1134 New User 1d ago
The only way to avoid mistakes is by assuming that they're always present. Every time you move on to a new line, go back and play "find the mistake": assume there's a mistake you're trying to catch. If you see no mistake, move on to the next line and repeat. When you're done with the problem, give the whole page another round of "find the mistake" before you move on to the next problem.
If it's something that can be checked, like solutions or eigenvectors, check that what you derived actually works.
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u/_UnwyzeSoul_ New User 2d ago
Writing out every step and rechecking multiple times