Proving the matrix inverse formula with cofactors

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James Cutler
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This one, prove it please, I have 5 problems in linear algebra class as an assignment which I have to hand in next week's Monday and I don't know how to solve this problem, the last one;
[tex]A^-=\frac{(A_j_k)^T}{det(A)}=\frac{(A_j_k)}{det(A)}[/tex]

Thank you
 

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James Cutler said:
This one, prove it please, I have 5 problems in linear algebra class as an assignment which I have to hand in next week's Monday and I don't know how to solve this problem, the last one;
[tex]A^-=\frac{(A_j_k)^T}{det(A)}=\frac{(A_j_k)}{det(A)}[/tex]

Thank you

I don't know about everyone else, but your notation is not clear to me. Is this a matrix equation? Are you talking about an element of a matrix? Did you lose a 1 on the left hand side? Did you mix up the indices somewhere?
 
for reaching out for help with your linear algebra assignment. Solving problems in linear algebra can be challenging, but with the right approach and understanding of the concepts, you can successfully complete your assignment. Here are some tips to help you solve your problems and prove your solutions:

1. Understand the concepts: Before attempting to solve the problems, make sure you have a clear understanding of the concepts involved. This will help you identify the correct approach to solving each problem.

2. Review class notes and textbook: Go back to your class notes and textbook to refresh your memory on the relevant topics. Look for examples and practice problems that are similar to the ones in your assignment.

3. Start with simpler problems: If you are struggling with a particular problem, try starting with simpler versions of it. This will help you build your understanding and confidence before tackling the more complex problems.

4. Use online resources: There are many online resources available that can help you with linear algebra problems, such as video tutorials, practice quizzes, and step-by-step guides. Take advantage of these resources to supplement your learning.

5. Collaborate with classmates: Consider working with classmates to solve the problems together. This can help you learn from each other and approach the problems from different perspectives.

As for the last problem in your assignment, it involves finding the inverse of a matrix. Remember that the inverse of a matrix A is denoted as A^-1 and is defined as A^-1 = (adj(A))/det(A), where adj(A) is the adjugate (transpose of the cofactor matrix) of A. Using this definition, you can solve the problem by finding the adjugate of A and dividing it by the determinant of A.

I hope these tips will help you in solving your linear algebra assignment. Remember to start early and seek help if you are stuck on a particular problem. Good luck!