Trefor Bazett, at 2:21 you say that the condition for "x" is that it is NOT equal to 0, yet you didn't write it in your notes... Just wanted to point that out for everyone else too
Instead, he wrote that x is equal 0... and calls it a homogeneous system(meaning it IS zero). Contradicting it, he also previously mentioned (ua-cam.com/video/4wTHFmZPhT0/v-deo.html) that "It is silly to think of zero vector as an Eigenvector… so exclude this possibility" - Trefor. Confusing to learners, hopefully, someone can help correct this.
With your explanation, this equation and why we use that particular method for finding eigenvalues finally clicked. And just in time for the exam :) thank you!
I believe there's no video in the playlist about the meaning of summing matrices and the distributive property applied to matrices in the way shown at 2:00
(Written just for the sake of it, read it with caution) First note that we know that A(b+c) = Ab +Ac where the small letters b & c are vectors, and the capital letter A is a matrix Proof by trefor: ua-cam.com/video/KmDVM7VHB0Q/v-deo.html Now, let us define matrix addition, in the way it is regularly defined, for matrices A, B, C of the same dimension: A+B = C where Cij = Aij + Bij Now let's see which properties this new operation holds We have to prove this: Ax + Bx = (A+B) x (where again, smaller case x is a vector) This is very easy too prove algebraically, in a similar fashion to the video of the proof of the previous property i linked (expand the matrices and multiply the terms to see what's going on yourself...), it's hard to write down in a comment graphically! Done this we want to prove that the same properties hold, but with matrices and not vectors AC + BC = (A+B) C Proof: AC + BC = [Ac1 ... Acn] + [Bc1....Bcn] = [Ac1 + Bc1 ... Acn + Bcn] = [(A+B) c1 ... (A+B) cn] = (A+B) C And then we can also prove the other one A (C+D) = AC+ AD Proof: A (C+D) = [A (c1+d1) ... A(cn + dn)] = [Ac1 + Ad1 ... Acn + Adn] = AC + AD
I would love if you had some resources to do practice problems for the courses you are explaining. I’ve been having trouble in my linear algebra class(mostly just not able to understand the teacher) and you have been so helpful in helping me learn the material. My grade has definitely been boosted a letter grade or two. Thank you so much.
For those wondering how we get to infinite solutions refer this previous video : ua-cam.com/video/OFALIHBY5Bw/v-deo.html Also learn about pivot variables and pivot columns
Trefor Bazett, at 2:21 you say that the condition for "x" is that it is NOT equal to 0, yet you didn't write it in your notes... Just wanted to point that out for everyone else too
Instead, he wrote that x is equal 0... and calls it a homogeneous system(meaning it IS zero).
Contradicting it, he also previously mentioned (ua-cam.com/video/4wTHFmZPhT0/v-deo.html) that "It is silly to think of zero vector as an Eigenvector… so exclude this possibility" - Trefor.
Confusing to learners, hopefully, someone can help correct this.
With your explanation, this equation and why we use that particular method for finding eigenvalues finally clicked. And just in time for the exam :) thank you!
We need teachers like him. Great
Very tough subject indeed. I am sticking with this. Math, chess and programming are wonderful for the 🧠
I believe there's no video in the playlist about the meaning of summing matrices and the distributive property applied to matrices in the way shown at 2:00
I managed to prove them, i'll write it down in case anyone needs it, hoping it ain't wrong xD
(Written just for the sake of it, read it with caution)
First note that we know that
A(b+c) = Ab +Ac
where the small letters b & c are vectors, and the capital letter A is a matrix
Proof by trefor: ua-cam.com/video/KmDVM7VHB0Q/v-deo.html
Now, let us define matrix addition, in the way it is regularly defined, for matrices A, B, C of the same dimension:
A+B = C where Cij = Aij + Bij
Now let's see which properties this new operation holds
We have to prove this:
Ax + Bx = (A+B) x
(where again, smaller case x is a vector)
This is very easy too prove algebraically, in a similar fashion to the video of the proof of the previous property i linked (expand the matrices and multiply the terms to see what's going on yourself...), it's hard to write down in a comment graphically!
Done this we want to prove that the same properties hold, but with matrices and not vectors
AC + BC = (A+B) C
Proof:
AC + BC =
[Ac1 ... Acn] + [Bc1....Bcn] =
[Ac1 + Bc1 ... Acn + Bcn] =
[(A+B) c1 ... (A+B) cn] =
(A+B) C
And then we can also prove the other one
A (C+D) = AC+ AD
Proof:
A (C+D) =
[A (c1+d1) ... A(cn + dn)] =
[Ac1 + Ad1 ... Acn + Adn] =
AC + AD
I would love if you had some resources to do practice problems for the courses you are explaining. I’ve been having trouble in my linear algebra class(mostly just not able to understand the teacher) and you have been so helpful in helping me learn the material. My grade has definitely been boosted a letter grade or two. Thank you so much.
For those wondering how we get to infinite solutions refer this previous video : ua-cam.com/video/OFALIHBY5Bw/v-deo.html
Also learn about pivot variables and pivot columns
Nice explanation. Thanks
Sir can i found eigenvector by determininate?
Not eigenvalue l mean
If you give an example your vedio become so usefull
Thank you for what you give
Multiply I to both sides
Describe with a example ...how can we find the eigen values of a matrix if the determinant is given.....
I wonder why you keep writing the condition x is NOT equal to zero as x = 0.