Decomposing Matrices into Elementary Matrices: A Reverse Approach

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To express matrix A as a product of elementary matrices, one can reverse the process used to find A's inverse. If A-1 is represented as the product of elementary matrices E3, E2, and E1, then A can be expressed as A = (E3E2E1)-1, which simplifies to A = E1-1E2-1E3-1. This method effectively utilizes the relationship between a matrix and its inverse in terms of elementary matrices. The discussion highlights the importance of understanding the connection between a matrix and its inverse when decomposing them into elementary matrices. Clarifying the approach ensures accurate representation of A in the desired form.
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I have a question about elementary matrices,
I have matrix A, and I just found A-1, and then the question wants me to write A-1 as a product of elementary matrices.
Ok, that's easy, but now the question wants me to write A as a product of elementary matrices, how do I go about doing this?
Would it be the same as writing A-1 as a product of elementary matrices but backwards?
 
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lol does that question make sense? or should I describe it better?
 
If A-1=E3E2E1, then A equals the inverse of that; that is A=(E3E2E1)-1=E1-1E2-1E3-1.
 

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