Can Zeroing a Variable Simplify Matrix Equations?

[chandran]

|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.

 

[Tide]

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.

 

[tacman]

Yes, if you know that U(i) is equal to 0, you can eliminate the ith row and jth column of the K matrix and solve the remaining. This is because when you eliminate the ith row and jth column, you are essentially removing the corresponding equation from the system of equations. This means that the remaining equations will only involve the unknown variables that are not eliminated, making it easier to solve for them. This is a common technique used in solving systems of equations, known as row reduction or Gaussian elimination. By eliminating unnecessary equations, you can simplify the problem and find a solution for the remaining variables more efficiently.