Sir, You are awesome..I mainly came here to learn how to find the solution to a matrix raised to a power. But you taught me fundamental concepts I have forgotten a long time ago. Thanks so much. 😀
What about the very simpler and immediate way which involves matrix decomposition with eigenvalues and eigenvectors? With this you won't have to distinguish positive and negative powers...
Great observation! As I mentioned at the end of the video, diagonalizing the matrix using eigenvalues & eigenvectors is another effective way to compute powers of a matrix. I'm planning to dive into this topic, including how to diagonalize a matrix and utilize eigenvalues and eigenvectors, in a future video. Stay tuned for that, and thanks for watching😇
Indeed, however the proposed formula is just a guess, and it could be wrong. The problem statement says "guess a formula" so I suppose it's okay to accept the solution and stop there. If you would like to be sure that it's the correct formula you could proove it i.e. by induction, that's what I wanted to convey with my previous comment.
@@ventus365 It is absolutely fine to solve it this way since it is guessing not proving. Also, this kind of question in Linear Algebra course is usually solved this way and it is a popular question in the course. Of course in math usually accepted different kinds of answers as long it satisfies the requirements 😊
You have to see the pattern similar to what I have done in this video by guessing about the power of the matrix. For example, compute A^2 then A^3, and if it is necessary to compute A^4 as well, where A is any given square matrix. Another way to compute a power of a matrix which I will do at some time in the future doing diagonalize the matrix to compute A^n, where A is any given square matrix and n is the integer number that you want to compute.
q.i/ in the following linerr system determine all values of k for which dhe resulting linear system has: (1) no solution (2) a unique solution (3) infinitely many solutions. x_(1)+x_(2)+x_(3)=2 x_(1)+2x_(2)+x_(3)=3 x_(1)+x_(2)+(k^(2)-5)x_(3)=k ........ Note .X_(1). X_(n)=x1 or x2
@@halgordamirsalh399 I think your question is not related to this video, and it is not clear for me, this X_(1). X_(n)=x1 or x2. However, your question is related to these videos in my playlist: ua-cam.com/video/gPOL-hwzIUc/v-deo.html ua-cam.com/video/61vt1nDHOKo/v-deo.html I think the best way to solve it is by put the equation as a linear system, like this x_(1)+x_(2)+x_(3)=k 2 x_(1)+2x_(2)+x_(3)=k 3 x_(1)+x_(2)+(k^(2)-5)x_(3)=k Then at the end you have to take the solution which satisfy this equation, X_(1). X_(n)=x1 or x2.
Thank you so much sir, you are a life-saver
Glad it helped & Good luck👍
Sir, You are awesome..I mainly came here to learn how to find the solution to a matrix raised to a power. But you taught me fundamental concepts I have forgotten a long time ago. Thanks so much. 😀
Glad you liked it! Your support keeps me motivated to create more 👍😇
Love you sir from India ❤
Thank you so much for your kind words & I'm glad you enjoyed the video 😇
What about the very simpler and immediate way which involves matrix decomposition with eigenvalues and eigenvectors? With this you won't have to distinguish positive and negative powers...
Great observation! As I mentioned at the end of the video, diagonalizing the matrix using eigenvalues & eigenvectors is another effective way to compute powers of a matrix. I'm planning to dive into this topic, including how to diagonalize a matrix and utilize eigenvalues and eigenvectors, in a future video. Stay tuned for that, and thanks for watching😇
this was really helpful, thank u
Glad it was helpful!
You could try to prove the general formula of A^n by induction.
In math, there are many ways to solve the problem & glad to hear another way to solve the problem! 😇
Indeed, however the proposed formula is just a guess, and it could be wrong. The problem statement says "guess a formula" so I suppose it's okay to accept the solution and stop there. If you would like to be sure that it's the correct formula you could proove it i.e. by induction, that's what I wanted to convey with my previous comment.
@@ventus365 It is absolutely fine to solve it this way since it is guessing not proving.
Also, this kind of question in Linear Algebra course is usually solved this way and it is a popular question in the course.
Of course in math usually accepted different kinds of answers as long it satisfies the requirements 😊
Good Channel!
Thanks, and glad it helped 😇
Thanks
You are welcome & thanks for watching 😇
How to solve if the elements are not 1
You have to see the pattern similar to what I have done in this video by guessing about the power of the matrix. For example, compute A^2 then A^3, and if it is necessary to compute A^4 as well,
where A is any given square matrix.
Another way to compute a power of a matrix which I will do at some time in the future doing diagonalize the matrix to compute A^n,
where A is any given square matrix and n is the integer number that you want to compute.
@@Mulkek Thank u
@@cowboy3570 You are so welcome & Good luck👍
hi Mr please 🥺 helping me
Hi, I am happy to help, and let me know how I can do that 😊
@@Mulkek thanks mr.
q.i/ in the following linerr system determine all values of k for which dhe resulting linear system has: (1) no solution (2) a unique solution (3) infinitely many solutions. x_(1)+x_(2)+x_(3)=2 x_(1)+2x_(2)+x_(3)=3 x_(1)+x_(2)+(k^(2)-5)x_(3)=k
........ Note .X_(1). X_(n)=x1 or x2
@@halgordamirsalh399 I think your question is not related to this video, and it is not clear for me, this
X_(1). X_(n)=x1 or x2.
However, your question is related to these videos in my playlist:
ua-cam.com/video/gPOL-hwzIUc/v-deo.html
ua-cam.com/video/61vt1nDHOKo/v-deo.html
I think the best way to solve it is by put the equation as a linear system, like this
x_(1)+x_(2)+x_(3)=k
2 x_(1)+2x_(2)+x_(3)=k
3 x_(1)+x_(2)+(k^(2)-5)x_(3)=k
Then at the end you have to take the solution which satisfy this equation,
X_(1). X_(n)=x1 or x2.
@@Mulkek ok mr thanks 🙏