Finding matrix and the inverse is given

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    Inverse Matrix
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Homework Help Overview

The problem involves finding a matrix A given the equation (I+2A)⁻¹ = [[-1, 2], [4, 5]]. The context is linear algebra, specifically dealing with matrix inverses and operations.

Discussion Character

  • Exploratory, Problem interpretation

Approaches and Questions Raised

  • Participants discuss reversing operations on the inverse to isolate A. There is an emphasis on understanding the implications of the inverse on the left side of the equation.

Discussion Status

Some participants have provided guidance on how to approach the problem by suggesting to work through the inverse step-by-step. There is a sense of progress as one participant expresses newfound clarity in their understanding.

Contextual Notes

One participant indicates a lack of initial understanding and expresses confusion regarding the inverse operation, highlighting the challenge of the problem setup.

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Homework Statement



Using the following information, find the matrix A

(I+2A)-1 =

[-1 2]
[4 5]

Homework Equations



AA-1 = I

The Attempt at a Solution



none. I have no idea how should I start. The inverse on the whole left side is driving me crazy.
 
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Start reversing the operations of (I+2A)-1 one by one till you strip it down to A. You know the matrix value of (I+2A)-1
 
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FactChecker said:
Start reversing the operations of (I+2A)-1 one by one till you strip it down to A. You know the matrix value of (I+2A)-1

Thanks a lot for the response, so basically start getting the inverse of the given matrix and get rid of the -1 on the left then and keep going, is that what you mean ?

Sounds logical, not sure why I never thought of it that way. Again thank you.
 
That's right.
 
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Solved and understood. Thanks again :)
 

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