Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors - Example 2

Finding the Inverse of a 3x3 Matrix Using Determinants & Cofactors - Full Example
This video provides a comprehensive guide to finding the inverse of a 3x3 matrix using the methods of determinants and cofactors. Learn how to calculate the determinant, find the cofactor matrix, and use them to form the inverse with all steps explained clearly.
2x2 Determinant
( • Determinant of a 2 x 2... )
Solve 3x3 System Using Inverse
( • ❖ Solving a 3 x 3 Syst... )
What You Will Learn:
How to break down the process of finding the determinant of a 3x3 matrix.
The step-by-step calculation of cofactors for each element of the matrix.
How to construct the adjugate matrix from the cofactor matrix.
Insights on how the inverse matrix is used to solve systems of equations and other linear algebra problems.
If you find this video helpful, please subscribe, leave a comment, like, and share with friends or classmates studying linear algebra!
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You are awesome! I searched the web for nearly one hour and I ended up getting the transpose of the adjoint matrix. Finaly, you explained that you have to reflect the elements about the main diagonal (transpose it). Thanks a lot dude!

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Thanks again! So much easier than the textbook

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[@opticaldream]

thanx for helping us to understand it much easier i just had one question about the transpose before the last step what about it because the lecturer taught us to transpose the matrix and then multiply by 1/|A|

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I love the work in general. I am a critic by nature, and so this is said as someone who appreciates your work. Unless a test said to distribute I never would (in fact I would do the opposite, factoring out anything I could), and I certainly wouldn't reduce fractions so that they had different denominators (again, I might, if I felt it was needed do the opposite, and set things to common denominators). 1/66A where A has integers is much easier to work with than A where every value is /66.

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[@patrickjmt]

thanks for the kind words :)

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Great example. Much appreciated

[@childrenofgod423]

If the determinant is = 0 then there is no inverse, for all those wondering

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[@fuahuahuatime5196]

Hey Patrick, awesome videos. But why don't you mention adjoint matrices and transposing matrices in the title? It'll help a lot of students like me who are trying to study straight from the books. Thanks!

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[@alhaert]

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[@Kocis19]

Hey Patrick, does it matter which row you use to expand off the beginning and find the determinant?

[@keechthebeech4061]

I have a question, when finding the determinant does it not matter what row you choose going diagonally? or are you supposed to use all the rows.

[@rochranomajeccavea]

Hi Sir Patrcik, is thistopic also about the adjoint of a matrix right?

[@4kx]

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[@herman908]

Would it be simpler to use the Gauss-jordan method for a 3X3 matrix?

[@googoomoomooxD]

When doing the cofactor matrix, my textbook places the determinantes on the first column rather than the first row. Does this change my answer?