Adjugate Matrix Computation 3x3 - Linear Algebra Example Problems

[@dianampm99]

Your content is amazing. I am studying in a different country and even though most terms are different, the way you explain makes it "universally" understandable, if that makes any sense. Thank you so much. It is definitely the best content out there.

[@AdamPanagos]

Thanks so much for the kind words and glad I could help. Where are you studying?

[@dianampm99]

@@AdamPanagos Portugal!

[@chisangamulenga5984]

Great video,quite easy to understand. Thank you

[@AdamPanagos]

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

[@ToanNguyen-zp2wt]

Thank you so much. I read about adjugate matrix in wiki but not understand at all. Your clip helps me for my next math exam. Thank you !

[@AdamPanagos]

You're very welcome, thanks for watching. Hope that exam went well! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@MikalAndre]

C in row 2 column 3 is actually wrong. It's C32, not C23 which appears twice in your drawing.

[@AdamPanagos]

+Archangel Can you clarify maybe? The adjugate matrix is the transpose of the cofactors so the element in row 3 column 2 is supposed to be C23. I don't think there's any error but I could be wrong......

[@MikalAndre]

+Adam Panagos you're right, but the element in the third column is also listed as C23 in the chart. It's probably just a typo

[@peterjiang9828]

@@AdamPanagoshe was asking about row 2 column 3 but you answered row 3 column two, should row 2 column 3 be C 32?

[@Airknightangel]

Thank you very much, mister Panagos. Ευχαριστώ!

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@leahherrera8557]

Thank you for posting this! I think I understand better, but why don't we multiply the cofactor by the determinant for the new adjugate values?

[@EsperanceBG]

Thank you so much!!!!!!

[@AdamPanagos]

+EsperanceBG You're welcome, thanks for watching!

[@narendraparmar1631]

Thanks bro

[@ElifArslan-l9g]

thank you

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@gravygod9820]

Thanks!

[@AdamPanagos]

You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.

[@BLDabderrahime]

uhhh ?? you inversed the i with j i for the row and j for the column

[@AdamPanagos]

No, I didn't. The adjugate matrix is the transpose of the co-factor matrix. This matrix is being filled in correctly.

[@openeyes977]

I am watching this video from india😊

[@chandralekhachowdhury928]

Well this is wrong we need to transpose the final matrix to get the Adjoint.

[@AdamPanagos]

No, I'm sorry but I think you're wrong. The adjoint/adjugate matrix is the transpose of the co-factor matrix. I've directly computed the "already transposed" co-factor matrix so the final answer is correct. For example, cofactor c12 appears in row 2 column 1 instead of row 1 column 2 (i.e. the matrix I wrote out was already transposed). Right?

[@DrPerky1234]

the (adjugate / adjoint) matrix is the transpose of the cofactor matrix as in [C]^T . I believe this video correctly shows the (adjugate / adjoint) matrix calculation, as the final answer is infact the transpose of the cofactor matrix [C] i.e. in [C] the rows become the columns to create [C]^T. This is why you can see that the first row of the answer is C11, C21, C31.

[@chess_master_2150]

Your answer is not correct A13 is A31 and etc

[@AdamPanagos]

This video computes the adjugate matrix. It's correct. The adjugate matrix is the transpose of the cofactor matrix (and the transpose of the adjoint matrix). I think you're thinking of a different matrix.

[@skiplangly6591]

Nah this is incorrect, you can literally put this into a matrix calculator online and it will give you a different matrix. Your cofactors positioning is also incorrect, it should go C11 C12 C13 in the top row and C21 C22 C23 and so on in the next rows. You also have to transpose the cofactor matrix after finding it (switching the rows and columns)

[@AdamPanagos]

I think you're confused about what computation is being performed here. This video computes the adj(A), the adjugate matrix of matrix A. The adjugate of a matrix is the transpose of the cofactor matrix. That's why the ordering listed in this video (that writes out the transposed co-factor matrix and then fills it in) is correct. The transpose has already been computed. Hope that helps, Adam