#Preparing for Math Exam - Part 1 | Linear Algebra

121 messages · Page 1 of 1 (latest)

willow mauve
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Hello everyone, I am on the verge of finishing my university with only 3 exams left before graduation. Math 1 and 2 and Discrete Math 2.

I am not very good in Mathematics but I try my best so I apologize if I do not understand terminology or these questions and their solutions quickly.

For now, I am studying Math 1, I've been handed 57 questions by the professor in order to do good in the exam. 5 of those questions are Linear Algebra
One of those 5 variations will land on my exam, so I will need to learn those 5.

I am creating this post so that I can learn these faster with the help of this community instead of waiting for my professors replies (unfortunately, he isn't very communicative and does not reply). I've tried reaching colleagues for help but I didn't receive any help.

If anyone is curious, I will also insert the 57 questions which I have received as PDF file. I sincerely apologize since the document is written in Albanian and not in English.

Thank you for taking time to read this.

image.png 📎 MATEMATIKE_1_-_DETYRA_PROVIMI.pdf
terse pondBOT
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willow mauve
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This is what I have come up so far. I went up and wrote the number I multiplied it with on the side, instead of writing Rx > Rx + Rx

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Could this way of writing be considered wrong in any way whatsoever ?

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I saw it on a Youtube video from a tutor who was explaining the Gaussian Elimination and he wrote it himself like that so I also went ahead in the same format hahah.

earnest harness
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the standard method is to do, say (not for this problem specifically) 2I+3II->new matrix

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hmm

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let me see if i can latex it to show what i mean

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$\overbrace{\to}^{2I+3II}$

fickle heronBOT
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temu mod | promote to mod pls

1245133657690214403.png
earnest harness
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obviously with a longer arrow but you get what i mean

willow mauve
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Yeah alright, thanks.

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What about, the part where I am stuck

earnest harness
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in your working?

willow mauve
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Yes

earnest harness
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lemme see

willow mauve
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The only number to multiply -3 by and -8 in order to get 0 is 8/3 ? right?

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Or is there a better way?

earnest harness
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so, like, -3(8/3)-8 or what?

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lemme see

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row echelon form or reduced?

willow mauve
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Are you referring to a method

earnest harness
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like what form do you want it in

willow mauve
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Isn't this form that I did based from the image, called Gauss Elimination Method?

earnest harness
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something like $\begin{bmatrix}a&b&c&d\0&e&f&g\0&0&h&i\0&0&0&j \end{bmatrix}$?

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uh oh

fickle heronBOT
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temu mod | promote to mod pls

1245133657690214403.png
willow mauve
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Yes that is what I was trying to achieve, now I don't know which method is best used to solve this question the easiest.

earnest harness
earnest harness
willow mauve
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Okay alright, whichever form you think is best, consider me an amateur at this

earnest harness
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lemme see

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what i recommend from that third step is to get the a_(42) entry equal to zero

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so multiply the third row by 8 and the last row by 3

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subtract

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it’s gonna be some large numbers

willow mauve
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Yep

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Okay wait

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So when we multiply two rows, each of the following numbers of the both rows get multiplied by that number correct?

earnest harness
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yes

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scalar operation on the entire row

glacial seal
willow mauve
glacial seal
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I assume you meant II - I, III - 2I, IV - 3I? If so, then yeah, that's a correct first step.

willow mauve
earnest harness
glacial seal
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As are II, III and IV.

earnest harness
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you change the row that you want to be changed

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but only a singular row

willow mauve
willow mauve
earnest harness
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yeah

glacial seal
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I'd do it as II*8, IV*(-3).

earnest harness
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but here it’s 8II-3IV

glacial seal
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Oh.

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Yeah, you shouldn't combine operations like that.

earnest harness
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where you want to change the IVth row

glacial seal
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Even if it works, you might get confused.

earnest harness
earnest harness
glacial seal
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Anyway, when you finish this example, I can try showing how I would do it. There are several approaches to Gauss's method, after all.

willow mauve
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Row 2 numbers were: (before multiplication by 8) : -3 4 -2 -5

Row 4 numbers were: (before multiplication by -3 ) : -8 7 -4 -20

glacial seal
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Oh, I see how you're trying to do this.

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Not my preferred approach, but it still works.

willow mauve
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Oh alright, if theres a better and easier method over my complicated one, please go ahead no worries at all

glacial seal
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Oh, no-no, don't worry.

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Finish up with this approach first.

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It's not like one is worse than the other, they are just a bit different in how exactly you perform row opeations.

willow mauve
# willow mauve

Okay so yes, I came up with this result after the multiplication of rows :

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And now I'm going to achieve the last 0

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I may have calculated something wrong

willow mauve
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Let me just re-do that part first again, sorry

glacial seal
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Well, we're going to need the full solution to check it.

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(as in, each transition with operations denoted so it's understandable what's being done)

willow mauve
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Here I did it from the beginning and hopefully more descriptive

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I apologize for my handwriting

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I still have one final 0 to go, I just wanted to show you this method maybe its more explanatory

glacial seal
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What does ± mean here?

willow mauve
glacial seal
willow mauve
glacial seal
willow mauve
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How do I explain this uh

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You're absolutely correct

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ugh

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I have a better idea, in order to not take more of your time. Proceed with your methodology and I will simultaneously do mine

glacial seal
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Ah, ok.

willow mauve
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So the final table resulted it =

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1 2 -2 1 6
0 -24 32 -16 -40
0 0 -33 22 -44
0 0 0 34 4

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Let me know if yours came out the same too

glacial seal
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So yeah, -20 was correct that time.

willow mauve
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i corrected

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I just realized that this Rx things that I tried to describe is so poor

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Sorry, i tried

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I believe we will come to a conclusion once I will see your methodology

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I'm just going to get some food I will be back in 30 minutes, after we solve the first one, do you happen to have the time for the rest of them

glacial seal
willow mauve
willow mauve
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Though, the end result of your method and mine should be the same right?

glacial seal
clever hawk
glacial seal
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As I said, this method just tries to involve less fractions and big integers.

earnest harness
plush pecanBOT
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@willow mauve

:HelpIcon:| Help Reminder

Hello yellownimbus, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

willow mauve
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I apologize, I left it open just in case I still need it because I am still working with these types of equations.

plush pecanBOT
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@earnest harness @glacial seal @clever hawk The user still needs help with this help request.

willow mauve
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Didn't expect that it would ping you guys, for now I don't seem to be in a tight spot, but judging from the other questions that I still have not started yet, I may need assistance later on. So should I leave this thread on or should I close it?

glacial seal
earnest harness