Cayley-Hamilton Theorem: Inverse of 3x3 Matrix
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- Опубліковано 6 лют 2025
- How to find the characteristic equation of a 3x3 matrix and use this cubic equation for the matrix to find its inverse...an interesting application of the Cayley-Hamilton Theorem.
The only good video ive found on this topic. Listen at 1.5x speed and enjoy
@Tud: Thank you!
yes this is the only one and i was listening 1.5x before i even saw thissss!
Thanks 👍
Never heard of this concept before. All it took was 14min and 34sec to understand! Thank you very much for the clear explanation.
You're very welcome!
Thank you very much for this video! I didn't know how to use the theorem to find inverse and now its all clear. Please keep up the good work!
Thanks, will do!
Thanks Jay, I really enjoy this lesson , can not thank you enough for explaining the lesson in good and interesting way 😫💗.
@Super Lady: Happy to hear that!
Hi Jay, you helped me SO MUCH thank you from the bottom of my heart.
God bless you ❤️
Love ❤️ from Saudi Arabia 🇸🇦
You are so welcome!
Out of all the C-H videos i watched today, you are getting the like. Though i wasn't a fan of this method to find the characteristic
Thank you for your detailed feedback
Yup I'd much rather do it the traditional way of substracting the lambda's and finding the det but great vid nonetheless.
Thank you!
Extremely useful video, Thank you!
@Frank: Thank you!
Thank you I found a new method to use cayley hamilton theorem
That's great!
THANKS JAY YOU ARE VERY EASY AND BRILLIANT TO FOLLOW BUT HOW DO I DOWN LOAD
@Vincent: Thank you!
Great video! I'm curious, how did you find the formula for the characteristic equation? Is there a general trend for n by n matrices?
Yes: en.wikipedia.org/wiki/Characteristic_polynomial
Thanks!
You’re videos are amazing..keep it up🔥♥️
Thank you so much
you're a life savior
@George Philip: Thank you!
The sum is very much useful to me mam and thank you.
You are most welcome
good video.this video so helpfull for me my university acedemic
That's good to know
you shld become my ny maths teacher .... yu my hero😍😍😍😍😍😍😍
@Kenneth Sithole: Thank you!
Was helpful ☺ thank you so much
Thank you!
Umm....i have one more problem . I can calculate the matrix multiplications but I don't know the significane of that process. I mean, why do they have to be multiplied in the same fashion as we use and why not others. Those mathematicians would have surely developed it for worthier uses than getting just marks 😁😁😁😁
It would be a REAL BIG help.... Please help me
Matrices are useful in transformations, so are used in computer graphics; they can also be used as a way of writing n linear equations in n unknowns...these equations can be solved if the determinant of the matrix is not zero.
@@MathsWithJay not like this....I wanted to ask its geometrical significance.....like what happens when we multiply matrices
Awesome video, thank you so much!
Glad it helped!
thank you for your helpful video :)
Glad it was helpful!
Thanks from syria 🌷❤️
You're very welcome!
Fellow syrian 🙌
If the detA was 0 and you still had an answer, would the answer be valid?
Encountered a similar math
If the det is zero, there is no inverse
بارك الله فيك
Thank you!
how would you apply this method to a 2x2 matrix
ua-cam.com/video/rcNPErHczbE/v-deo.html uses the theorem to find the power of a 2x2 matrix
So briefly video
Thanks.
@Mohammad Mustafa: Thank you!
One thing I don't understand... why is lambda^3 positive? Surely the cube -Lambda will be negative?
At what time in the video?
@@MathsWithJay 0:45, the general formula states there is lambda to the power of 3 as positive. I have actually seen this elsewhere but I'm confused as to why it is the case.
I figured it out. I was trying to derive it from first principles with variables rather than numbers and got the reverse formula (-lamba^3 + trace(A)lamba^2 etc...). But then I realised the cubic formula is odd so f(-x) = -f(x) and thus the root f(0) = -f(0) and the two formulas output the same roots.
Sorry for the stupid question :D
I'm glad to see you've sorted it out - thank you for taking the time to explain - it may help someone else in the future.
Thank you!
You're welcome!
Why it is not shown here how derive this formula ?
I know how to do that
If one column is linear combination of two vectors we can write determinant as sum of determinants replacing column with that vectors
det([[a_{11},bv_{1}+cw_{1},a_{13}],[a_{21},bv_{2}+cw_{2},a_{23}],[a_{31},bv_{3}+cw_{3},a_{33}]]) = b*det([[a_{11},v_{1},a_{13}],[a_{21},v_{2},a_{23}],[a_{31},v_{3},a_{33}]])+c*det([[a_{11},w_{1},a_{13}],[a_{21},w_{2},a_{23}],[a_{31},w_{3},a_{33}]])
Cofactor expansion of determinant is also useful
You're awesome 👌🏿
Thank you!
hello. can you help me to proof the cayley-hamilton theorem for matrix m x n? thankyou
@Nurul Pratiwi: Are you trying to use this for a matrix that is not square?
@@MathsWithJay yes. I have a journal about that but i stuck on the proof:(
thank you .can you recommend a book about this topic?
@Pp Jj: What level are you studying?
@@MathsWithJay hello.thank you for your answer.i'm a PHD student of Mechanical engineering and looking for a book about matrix algebra.(actually,wondering how to solve a matrix equation like as: A^2+A+I=B that B and A both are matrix and B=[-1 2,60] )
Wouldn't B have to be a square matrix?
@@MathsWithJay yes it is a 2X2 matrix.
Is there a sound? Can't hear something
Yes, there is audio
Tnq you so muchhhhhh mam
@Shinu Sp: Thank you!
sum of the terms of the leading diagonal and det of A are calculated in same way..that's wrong!!! In DET|A| ..diagonal elements must be multiplied the corresponding determinants..
At what time in the video?
@@MathsWithJay 5:10-5:40..
How to do with a 5x5 matrix
en.wikipedia.org/wiki/Cayley%E2%80%93Hamilton_theorem generalises so may be useful
3 3 4
Q or A?
its 7I not 9I
@Heat Transfer: At what time in the video?
Maths with Jay 6.51 general form of equation it would have been 7I instead of 9I i think i didnt watch the solution I just found it 7I
Where did you find the "7" from?
@@MathsWithJay oh my bad im sorry ima fool there is no wrong about it