[Linear Algebra] Linear Combinations

We discuss linear combinations in linear algebra.
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We look at linear combinations and some example problems.
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[@MasayoMusic]

Thank you. Those True False questions are really helpful in consolidating the theories/axioms.

[@Venus-xg3li]

Thank you but I didn’t understand anything

[@jacobgarwin5616]

That "f" at 10:47 was glorious...

[@amiraahmed7267]

true :D

[@hawraalsayed3206]

how do you find that x2=2 and x1=7-2x2?

[@meet1348]

great explanation. Thank you

[@nuzrathrafiqbaloch7703]

Great Sir..really You Make Me Able To Understand What The Linear Combinations Are...thanksss

[@juniorcyans2988]

Every time I tried to answer the true or false questions and I always got at least one wrong 😑 I love your videos, easy to understand those key concepts❤

[@adewaleosobu3238]

I am watching your videos in 2021 and they are a blessing. Great Job!!!

[@pedramhaqiqi7030]

Hey trevtutor, i had a question based on the last true or false, so if column vector [2,1,3] is in R3 , is What about row vector [2,1,3] ? in addition what if the column vector is [2,1,0] is that in R2?

[@richardben-polo]

This was helpful but show your steps in your workings.

[@maxpercer7119]

there is a small mistake @ 3:50 , it should be
[-1 -2 ] [ -7 ]
[2 -5 ] [x1] = [ -4 ]
[5 -6 ] [x2] [ 3]

[@louisleemans3982]

I think you just saved my exam

[@nisala00]

really great explanation. really You Make Me Able To Understand What The Linear Combinations Are...thanks

[@alisyed6830]

5:47 how do you get the x2 =2 ? Is x2 in the second column? Is this matrix augmented?

[@nipunasarathchandra9984]

yes.by 2nd row he got 0.x1 + 1.x2 = 2.therefor x2 = 2.

[@statube9982]

It is a good video. But from the last three t/f questions the second one is true. Why I said true is, what if the vector V2 you said is not a zero vector when it is multiplied by another scalar. You should general for any vectors addition and multiplied by any scalar. You said specifically 1/2*V1 + 0V2 = 1/2V2, what about 5V1 + 9V2 ? or else ?

[@maxpercer7119]

True or false, another notation for the (column) vector
[1]
[2]
is (1,2). I choose true.
Also i think vectors are defined as column n x 1 matrices.
Vectors are column vectors, not row vectors.

[@sushmitanigam4979]

superb explanation. thanx a lot.

[@jenniferpramana9136]

For the last example where x3 is free, does this mean the system has infinitely many solutions?

[@obww306]

yes, sir

[@IanXiWan]

Blew me away in two minutes.

[@BitsToBytes92]

Thank you!

[@ThePCxbox]

your second major example confuses me. So for a linear combination, you dont have to include all given vectors in a solution? was the third vector put there as a "this is just another vector to help you solve this exam question" type of thing?

[@mrmister3507]

You are amazing, thanks a lot for these videos!

[@swojnowski8214]

It is an operation.

[@rahuldas6777]

hm? you can eliminate a row if the row above is identical to it?

[@jenromeave4793]

how tf did you get x sub 1= 2?

[@maysamshafayee218]

تشکر

[@Rahul-yu3ro]

6:48 (timestamp for me)

[@muhammadarifbinmohdanuwa9960]

good

[@tashnimasgar7227]

Could you explain for true or false how is v1+v2=(1/2)v1?

[@ThePCxbox]

From what I gather, he isnt saying that he is adding v1 + v2, hes saying v1 and v2 are simply given vectors and a linear combination is just a scalar times a vector. Since there isnt a solution that you need to solve (theres no "prove a combination of these 2 vectors equals vector b) given these vectors you could theoretically multiply anything by any of those 2 vectors and it would be correct because the "vector b" is up to us in this instance and trevtutor decided that whatever vector b was, it was equal to half of vector 1.
Atleast thats what I gathered. Dont quote me though.

[@indrajitnandi8760]

in your first problem on true and false,u said that both the representations are different. But any column vector can be represented as a row vector and if taken in that sense both the vectors will be equal.So why they are considered to be different vectors?

[@Trevtutor]

"But any column vector can be represented as a row vector". They're not the same vectors though. One is a column vector and another is a row vector. By definition of a vector, we would have to write [2 1]^(transponse) for it to be the same notation as the column vector.

[@NubcackeRider]

bad