Linear Algebra: 30 True or False Questions

[@DrValerieHower]

Here is a blank copy of the T/F in this video: drive.google.com/file/d/1wzWNOL5EI6Q2jgT5rt5fyUvkefhg4y_k/view?usp=sharing

[@flergusblergus6966]

Great video!

[@DrValerieHower]

Thank you so much!

[@Karim-nq1be]

Great video, was very useful and enjoyable, thank you very much!

[@DrValerieHower]

You are welcome!! I am glad to hear this video is useful for you. :)

[@davidmurphy563]

Oh no... I just got no. 7 wrong. Got everything right up to that point at 7:00 I reasoned that the vectors would for a 2 x 3 matrix and no being square you would have a free column. I get your logic but since when do you combine two vectors with like components and it not make a matrix? Really enjoying the test though. I've never formally studied the topic - just used it for coding and whatnot - so I have to reason everything though. Right, I'll battle on.

[@davidmurphy563]

The notation on Q10 is very confusing... No idea what T is, a transform of some sort? Anyway, I think you must be asking whether there's a 3x3 matrix which outputs the vectors. I'm not sure which is the output, is it the vector in the brackets or after the equals? I guess the latter. And does T mean these are the same matrix? I assume so. So starting on the right for no reason the matrix is obviously: {{0, 1, 0}, {0, 0, 0}, {0, -1, 0}} Well, that matrix just gives a zero vector multiplied by {3,0,0}. I'm not sure I understood the question.

[@davidmurphy563]

Listened to your explanation. Was T in both cases supposed to be the same vector or just two orthogonal vectors? I'm not clear on whether T() is a variable. Looks more like a function of some sort. Anyway, we agree that obviously they can't be transformed by the same matrix. Let's call that a win.

[@davidmurphy563]

Ugh, I'm stuck on 11 too. I don't know what "kernel" means... I'm going to guess and say it's when the span is reduced. So it's the RREF with the free variables removed. Well, A could be a zero matrix. So false. I'm not sure what kernel means but you can't get a non-zero vector out of a zero matrix.

[@davidmurphy563]

Nope wrong. I don't know what "nullity" means either. Obviously how much null. And obviously it's a rectangular matrix. Surely the rank can reduce to zero? Ugh, listen, I'm just guessing what these words mean. 9/11 so far. Not too bad a score. Let's press on.

[@davidmurphy563]

Ok 12 is a fascinating question. Nah, it's obviously false. The det is a measure of area. A R3 triangular matrix 3, 3, 3 has a RREF of the Identity. But the dets are 3 and 1 respectively. False, final answer.

[@RiteshArora-s9x]

The applications part questions in this book is very hard