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# Why Does My Solve Linear Equations VI Give an Unexpected Solution Vector?

Primary Software:
Primary Software Version: 2013
Primary Software Fixed Version: N/A
Secondary Software: N/A Problem:
I want to solve the equation AX = B for X, where A is the known matrix, X is the unknown vector, and B is the known vector. However, when using the Solve Linear Equations VI, the resultant B does not appear to be correct. When multiplying AX to check my result, I get a vector that is not B. Why does this occur?

Solution:
This can occur when the input matrix, A, for the Solve Linear Equations VI is singular. When this is the case, instead of solving the equation AX = B for X, LabVIEW finds the least-square solution which is the solution with the least square mean error. This is because there is no solution for AX = B.

To check if a matrix is singular, you must determine whether the determinant is zero. If the determinant is zero, the matrix is singular. The easiest way to check this would be to use a Determinant VI to obtain the determinant.

Shown below is a VI snippet that demonstrates how a singular matrix can give a misleading solution. The snippet also demonstrates how to use the Determinant VI to test and see if a matrix is singular. Related Links:
LabVIEW Help: Solve Linear Equations VI
External Link: Invertible matrix - Wikipedia, the free encyclopedia

Attachments: Singular Matrix Example.vi Report Date: 09/24/2002
Last Updated: 09/13/2013
Document ID: 2PNGS2A2

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