[Linear Algebra] Linear Combinations

[@MasayoMusic]

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

[@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

[@VenusRahaf]

Thank you but I didn’t understand anything

[@adewaleosobu3238]

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

[@maxpercer7119]

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

[@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.

[@sushmitanigam4979]

superb explanation. thanx a lot.

[@louisleemans3982]

I think you just saved my exam

[@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❤

[@richardben-polo]

This was helpful but show your steps in your workings.

[@VictorNaftaly]

In the gaucian process...where we are getting the zeros in the corner, can different people get different outcomes but with zeros in the corner

[@IanXiWan]

Blew me away in two minutes.

[@jenniferpramana9136]

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

[@obww306]

yes, sir

[@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?

[@mrmister3507]

You are amazing, thanks a lot for these videos!

[@BitsToBytes92]

Thank you!

[@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.

[@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 ?

[@rahuldas6777]

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

[@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?

[@swojnowski8214]

It is an operation.

[@jenromeave4793]

how tf did you get x sub 1= 2?

[@maysamshafayee218]

تشکر

[@Rahul-yu3ro]

6:48 (timestamp for me)

[@muhammadarifbinmohdanuwa9960]

good

[@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.

[@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.

[@NubcackeRider]

bad

[@nisala00]

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