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Inverse Matrices used to solve linear systems

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Problem1.How are the inverse Matrices used to solve linear systems. Explain in your own words with example.

Problem 2. In the matrix Algebra why does there have to be right and left distributive properties.

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The expert examines inverse matrices which are used to solve linear systems.

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Attached solution.doc. Both problems are solved and can be found in this document

Problem1.How are the inverse Matrices used to solve linear systems. Explain in your own words with example.
Answer:

Consider the set of linear equations

A11x1+A12x2+.................A1nxn= b1
A21x1+A22x2+.................A2nxn= ...

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