How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (I)
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- Опубликовано: 6 май 2023
- Eigenvalues and eigenvectors are important concepts in linear algebra .To find the eigenvalues and eigenvectors of a 3x3 matrix using augmented matrix and row operations, follow these steps:
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1.Given a 3x3 matrix A, find the characteristic equation by subtracting r times the identity matrix from A and calculating its determinant. This gives the characteristic equation = det(A - rI), where I is the identity matrix.
2.Set the equation = 0 and solve for r. The values of r that satisfy the equation are the eigenvalues of A.
3.For each eigenvalue λ, solve the system of equations (A - rI)U = 0, where U is the eigenvector corresponding to r. This can be done by forming an augmented matrix [A - r | 0], applying row operations to put the matrix in row echelon form, and solving for the variables using back substitution.
4.Normalize the eigenvector by dividing it by its length, so that the length of the eigenvector is 1. This is necessary because eigenvectors are only unique up to a scalar multiple.
Repeat steps 3 and 4 for each eigenvalue r to find all the eigenvectors of A.
By using the augmented matrix and row operations, finding the eigenvalues and eigenvectors of a 3x3 matrix can be made easier and less error-prone. It allows you to reduce the matrix to a simpler form and then solve for the variables systematically. With practice, you can become proficient in using this method to solve complex problems in linear algebra.
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (I)
• How to Find Eigenvalue...
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (II)
• How to Find Eigenvalue...
How to Find Eigenvalues and Eigenvectors for 2x2 Matrices (II)
• How to Find Eigenvalue...
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Great.. you make a difficult problem into a simple one.. thank you very much.
Thank you so much
You're most welcome
Thank you
You're welcome
really you give clear and understandable explanation!THANK YOU TOO MUCH FROM MY DEEP HEART!!
Glad it was helpful!
Excellent tutor!
Keep it up!
I have struggled alot to understand this operation until I reached real destination.
Thanks for watching. Please do share the link of the video on your social media platform.
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This is another question on 3x3: How to find Eigenvalues and Eigenvector
Ty sir❤
Highly welcome
i appreciate your work☺
It's my pleasure
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (I)
ruclips.net/video/Mk-wDFrsFR8/видео.htmlsi=Er_TmFrXdrFWC4kk
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (II)
ruclips.net/video/QtRjiHpopcQ/видео.htmlsi=fBGQ58VbAAYj18wp
How to Find Eigenvalues and Eigenvectors for 2x2 Matrices (II)
ruclips.net/video/x7YSDofUwHk/видео.htmlsi=DF9O0YzaEAUylSaK
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A minor comment ... 'Eigenvektor' and 'Eigenwert' were the original german terms for this ...
for some reason this was not translated to 'Selfvector' and 'Selfvalue' (which would be
the litteral translations) ... instead, 'Eigenvalue' and 'Eigenvector' were created.
The german 'Eigen' is pronounced like the english EYE followed by GENeration ...
(but the 'G' of generation as a plain 'G' (as in give) not as a 'DJ')
so the proper pronouciation for 'Eigen' would be the (pseudo-english) EYEGEN.
Thanks . I will update that for subsequent video. And also, it has been subtitled.
why you calculate square matrix only. please
make video non square matrix to find the eigenvalues and eigenvector
Highly noted. Thanks
Please what if u get a cubic equation and the answers of r are decimal
How do we factorize it
do you have an example for that? Most cases r is always an integer.
@@successade1664 Yes please I have an example
@@successade1664 First row(0,-2,8)
Second row (1,10,-13)
Third row(3,-6,-4)
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (I)
ruclips.net/video/Mk-wDFrsFR8/видео.htmlsi=Er_TmFrXdrFWC4kk
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (II)
ruclips.net/video/QtRjiHpopcQ/видео.htmlsi=fBGQ58VbAAYj18wp
How to Find Eigenvalues and Eigenvectors for 2x2 Matrices (II)
ruclips.net/video/x7YSDofUwHk/видео.htmlsi=DF9O0YzaEAUylSaK