109 Linear Algebra True or False Questions that Guarantee you ACE YOUR FINAL!

[@DrWeselcouch]

MISTAKES: Q23 should be False. For example v1 is the zero vector and v2, v3 are any two orthogonal non zero vectors. Good luck studying for you Linear Algebra Final! Check out my Linear Algebra playlist for more practice problems! kzbin.info/aero/PLscpLh9rN1Rfo0ifw9RZFoJ2Te2jk_pwX

[@davidmurphy563]

Q28. Does a diagonal matrixv with non-zero components scale. You said true but it could be the identity matrix in which case B is left unchanged/unscaled.

[@DrWeselcouch]

@@davidmurphy563 Good point. I personally would call that scaling by a factor of 1.

[@davidmurphy563]

@@DrWeselcouch That's exactly what I was told when I last asked for a raise. ;)

[@DrWeselcouch]

@@davidmurphy563 sounds like we might have the same boss!

[@davidmurphy563]

@@DrWeselcouch Last night's discussion with my teenage son on this went like this: Me: If you scale a number by 1 so that it doesn't change, are you actually scaling it? Son: Yeah. Me: So if you rotate something by zero degrees, then that's a rotation? Son: If you rotate something by 360 degrees, is that a rotation? Me: I concede the argument.

[@blackpenredpen]

This is going to be insanely helpful! I will recommend my former students to watch this since I don't teach linear algebra myself and haven't done it for over a decade. I will also watch it to review it for myself. Thank you!

[@blackpenredpen]

@@DrWeselcouch I am sure plenty!

[@hugopelegrin3693]

You were here way before, thank you for discovering me this channel, bprp

[@warguy6474]

legend

[@jaxrevfi1309]

This is great! I’m sure that this will go viral, and I would love to see this for Calculus too! Keep up the great videos! :)

[@neilbhutada9666]

This going to help students at UW-Madison because our mid-terms only consist of 10 T/F questions.

[@DrWeselcouch]

Good luck!

[@jakekatsikas721]

Really appreciate all the hard work you're putting in!! Really helpful stuff!

[@mathmylife982]

Such creative content Mike B!

[@eminbaybarstimurstudent3802]

I have a question on 82nd question, on 56:09, so what if our matrix is an orthogonal matrix, then A^T would be equal to A^-1, and the eigenvalues of A^-1 is 1/ λ. So wouldn't our eigenvalues change in this case ?

[@DrWeselcouch]

Nope! That just implies that the real eigenvalues of orthogonal matrices are plus or minus 1.

[@eminbaybarstimurstudent3802]

@@DrWeselcouch Right, I forgot that, thank you for answering and for this great content :)

[@DrWeselcouch]

@@eminbaybarstimurstudent3802 No problem! Good luck studying for Linear!

[@drpeyam]

Omgggg, how did you do 109 linear algebra true false questions in less than 75 mins 😂😂😂 I did 111 in more than 4 hours 😂😂😂

[@JiaxiWang-n8z]

how lovely to see u here

[@Andrew-jw2qs]

THIS IS AMAZING THANK YOU

[@DrWeselcouch]

No problem! Feel free to share it with your classmates too :)

[@timonau244]

This is very helpful, thank you

[@yashmane13]

Thank you so much! This is a very helpful resource

[@DrWeselcouch]

Great! Good luck studying for linear!

[@mathematicalpoetry6902]

Q23 in my opinion should be False, for example v1 is the zero vector and v2, v3 are any two orthogonal non zero vectors.

[@DrWeselcouch]

You're right, the question should say that v1, v2, v3 are nonzero.

[@jollux8035]

using this an hour before my final, legendary stuff here

[@moabdul-]

did it help?

[@jollux8035]

@@moabdul- yea i got all my theory problems right, i take computational so it wasn’t as bad, but really good for studying

[@moabdul-]

@@jollux8035 sounds good, thanks man

[@emilieholiday606]

Thank you!

[@owen00062]

Q62. The statement is true if A is in echelon form. It is not only true if A is in echelon form; consider A = [1, 0; 1, 1].

[@DrWeselcouch]

I don't think I follow. Wouldn't the rows of that matrix would form a basis for Row A?

[@owen00062]

@@DrWeselcouch Yes, and that matrix isn't in echelon form. Hence the rows of A are a basis for Row A if A is in echelon form, but not only if A is in echelon form.

[@owen00062]

Just to be clear, the statement by itself is false; the counterexample you gave shows that clearly. I was just questioning whether "This is only true if A is in echelon form" holds.

[@DrWeselcouch]

@@owen00062 Ahh I see, at first I thought the matrix you wrote was a 1x4 matrix not a 2x2 matrix. My mistake!

[@DrWeselcouch]

@@owen00062 You're right! The word "only" should not be there! "It's true if..." is what I should have said.

[@jasonbroadway8027]

Scenario: Suppose that you used the phrase "ONLY the trivial solution" in Question 10. My reasoning would indicate that such a statement would be true. The word "ONLY" changes the problem. You were right, but I like to stray from the beaten path to test my knowledge.

[@balasavenedintulashabalbeoriwe]

Thank you professor. I have a wonder about the question 12. You say that this would be true if A had a pivot position in every column. Do you mean every column as well as row? Because for example A = [1, 0; 0,1; 0,0] has a pivot in every column but b = (0,0,1) (a vector in R^3) has no solution, yes? Or is the question saying, if there is a solution, it must be unique?

[@DrWeselcouch]

You're right, I should have said row and column. Assuming there's a solution, then what I said is correct, but that's a slightly different question.

[@daray21]

i have a question on #56, isn't the 2nd column in the example linearly dependent to the first column?

[@DrWeselcouch]

Sure, but the first column is a pivot column. There is only one non-pivot column in the example so it's automatically LI with itself.

[@sakhiwosekunqobadlamini1593]

Could we get a calculus video that's just like this one please🙏🙏🙏🙏😭

[@battlemode]

Nice video. I'd prefer if there was a slightly longer pause between asking the questions and showing the answer, even a second longer, so I have time to pause and consider it before you reveal the solution.

[@DrWeselcouch]

Thanks for the feedback! I'll keep that in mind for my next T/F video. There is a PDF with all the questions in the description if you want to try the questions before watching the video.

[@ksaigon]

you're a legend

[@CuteLittleHen]

Question three is confusing, because what if the field is not infinite, such as field Z7?

[@DrWeselcouch]

Good point. You should assume that every question is referring to matrices with real entries unless stated otherwise.

[@Aeldrion]

Q23 is wrong, right? v1 could be 0, v2 wouldn't be a multiple of v1, you can take v3 linearly independent of v2, and {v1, v2, v3} wouldn't be linearly independent?

[@DrWeselcouch]

You're right. It should say that the vectors are nonzero.

[@jerryzhang2548]

1:01:51

[@DrWeselcouch]

Hmmmm

[@petersmith9138]

Interesting

[@DrWeselcouch]

Interesting indeed... 🤔

[@aashsyed1277]

Very very very very very very very nicely 😀😀😀😀🥰

[@tho_norlha]

Thank you, we will have 20 true false and 20 mcq in this final exam 😁 happy new year

[@DrWeselcouch]

Good luck! I'm sure this video will be very helpful to you then!

[@xbz24]

Tysm

[@swartzsteinswartzstein8809]

i have to go over a bunch of these lol

[@DrWeselcouch]

Are you taking linear algebra this year?

[@swartzsteinswartzstein8809]

@@DrWeselcouch next semester!

[@DrWeselcouch]

@@swartzsteinswartzstein8809 This is a great way to prepare!

[@DivyanshMMMUT]

Coming from BlackPenRedPen

[@DrWeselcouch]

Awesome! Hope you stay for a while!

[@JMac___]

I think question 103 is wrong by definition, need c1,c2 to be non-zero

[@DrWeselcouch]

I think it's correct. The zero vector is orthogonal to everything and the set of just the zero vector is an orthogonal set.

[@JMac___]

@@DrWeselcouch sorry, my textbook defines orthogonal set as a set of non zero vectors such that they’re pairwise orthogonal. That’s why I am confused. Thanks for the reply 👍

[@gatitoconsueter]

I miss MC vida 😢

[@akshitseth8613]

Hi