Finding Inverse of Matrix & Solving AB=C: Urgent Help Needed

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SUMMARY

The discussion focuses on finding the inverse of a matrix and solving the equation AB=C for matrix A, given matrices B and C. The user expresses confusion about row operations and the process of obtaining the identity matrix. The solution provided indicates that to find matrix A, one must compute A = CB-1, where B-1 is the inverse of matrix B. The key takeaway is that matrix division is not possible, but multiplication by the inverse is the correct approach.

PREREQUISITES
  • Understanding of matrix operations, specifically matrix multiplication and inversion.
  • Familiarity with the concept of the identity matrix in linear algebra.
  • Knowledge of row operations used to compute the inverse of a matrix.
  • Basic proficiency in solving linear equations involving matrices.
NEXT STEPS
  • Learn how to compute the inverse of a matrix using row reduction techniques.
  • Study the properties of matrix multiplication and the role of the identity matrix.
  • Explore the application of the formula A = CB-1 in solving matrix equations.
  • Investigate software tools like MATLAB or Python's NumPy for matrix operations.
USEFUL FOR

Students studying linear algebra, educators teaching matrix operations, and anyone needing to solve matrix equations in mathematical or engineering contexts.

Rizzamabob
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Ok, i missed the class on finding the inverse of a matrix, and i only have a little bit of an idea on exactly what row operations i can do, when i try to make the matrix = its identity.

Another question I am stuck on.
Q.

I have 2 , 3 X 3 matrixs B and C respectivly.
The question is find A if AB=C, and i know B and C
Now, i know i cannot divide matrix's, and I am stuck as to what way i should travel to find the matrix A.
Thanks guys ! :shy: :rolleyes:
 
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[tex]AB = C \Leftrightarrow ABB^{ - 1} = CB^{ - 1} \Leftrightarrow A = CB^{ - 1}[/tex]

You only have to find the inverse of B.
 

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