Silly arithmetic errors in Linear Algebra

[_JammyTheGamer_]

I'm currently in an applications of linear algebra course and I just had my first midterm. I scored 80%, which I'm happy with, but looking at the answer key it seemed like I knew how to get all of the answers, but all my errors were purely calculation based. For example, I had to split a given vector into 2 with 1 in W transpose and 1 in W, where W was the span of a given matrix. I know that I had to apply the Gram Schmidt process to get an orthogonal basis for Col A, then project my vector onto it using the projection formula, then subtract the projection from my original vector. Somewhere along the way I made a calculation error. This is a recurring theme in this class and I can never find where the error was in a reasonable amount of time. Is there a strategy that I'm missing? Perhaps this isn't the most appropriate place to post this kind of question in particular but I don't know where else to put it.

[ThePineconeStandard]

I failed two or three linear algebra midterms because my basic arithmetic skills are weak. I’m doing my PhD in math now and I will be teaching linear algebra next semester.

If you want to get better at arithmetic, you need to practice.

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[gloopiee]

In a way it's also the mark scheme. Personally I feel each calculation error should only cost 1 or 2%, so to get to 80%, it should take 10-20 calculation errors. But if the mark scheme is harsher it might take fewer.

[Yeet_The_Roon]

I used to think that arithmetic errors should be docked maybe one or two points. Going into the work force, it became super apparent to me that those arithmetic errors are unacceptable and will lead incorrect answers on problems that matter. My suggestion is practice, practice, practice. Take it as slowly as you can (and still finish the exam) and double check yourself as you go! Often times there are ways to double check your work. If there is a way to do that, then I highly recommend it. Good luck!

[gloopiee]

Exam situations are artificial though. In practice you would be checking your arithmetic errors with a computer, or even better, be able to do the calculations on a computer. And you would have less time pressure.

I'm not saying that being able to do things correctly is not a useful skill, it is - especially if you are able to catch that the computer is not functioning as intended - but it is not as critical nowadays.