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?
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?
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❤
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 ?
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.
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.
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?
"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.
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Thank you. Those True False questions are really helpful in consolidating the theories/axioms.
how do you find that x2=2 and x1=7-2x2?
That "f" at 10:47 was glorious...
true :D
I am watching your videos in 2021 and they are a blessing. Great Job!!!
Great Sir..really You Make Me Able To Understand What The Linear Combinations Are...thanksss
great explanation. Thank you
there is a small mistake @ 3:50 , it should be
[-1 -2 ] [ -7 ]
[2 -5 ] [x1] = [ -4 ]
[5 -6 ] [x2] [ 3]
5:47 how do you get the x2 =2 ? Is x2 in the second column? Is this matrix augmented?
yes.by 2nd row he got 0.x1 + 1.x2 = 2.therefor x2 = 2.
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
Thank you but I didn’t understand anything
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?
hm? you can eliminate a row if the row above is identical to it?
For the last example where x3 is free, does this mean the system has infinitely many solutions?
yes, sir
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?
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❤
I think you just saved my exam
superb explanation. thanx a lot.
Blew me away in two minutes.
Thank you!
You are amazing, thanks a lot for these videos!
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 ?
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.
how tf did you get x sub 1= 2?
This was helpful but show your steps in your workings.
Could you explain for true or false how is v1+v2=(1/2)v1?
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.
6:48 (timestamp for me)
تشکر
It is an operation.
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?
"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.
good
bad
really great explanation. really You Make Me Able To Understand What The Linear Combinations Are...thanks