Can Zeroing a Variable Simplify Matrix Equations?

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SUMMARY

The discussion focuses on simplifying matrix equations by zeroing a variable within a system of linear equations. Specifically, when a variable U(i) is known to be zero, the corresponding ith row and jth column of the K matrix can be eliminated, allowing for the resolution of the remaining unknowns with n-1 equations. This approach leverages the relationship between known and unknown variables in matrix systems, enhancing computational efficiency in solving linear equations.

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  • Understanding of linear algebra concepts, particularly matrix operations.
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chandran
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|F1| |K11 K12 K13| |U1|
|F2| = |K21 K22 K23| * |U2|
|F3| |K31 K32 K33| |U3|



I have the above matrix relating F K AND U .

In this F & k are known but u is unknown

Suppose i know U(i) is equal to 0 can i eliminate the ith row and jth column of the K matrix and solve the remaining. How this can be understood.
 
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You can understand it this way. Your matrix system represents a set of n linear equations in n unknowns. If the value of one of the unknowns is "discovered" then you need only n-1 equations to resolve the remaining unknowns. Obviously, the column corresponding to the resolved value can be eliminated if the value is 0. You get to pick which of the two remaining equations to keep.
 

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