How to solve a simple Matrix equation?
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Hello,
I have a small problem. I want to solve the multiplication of a given matrix.
For Example:
A = [-1,0,0,1;1,-1,0,0;0,1,-1,0;0,0,1,-1];
x = sym('x', [4,1]);
x(1,1)=1;
solve(A*x==[0;0;0;0])
Because I am a beginner at Matlab, I really don't know what im doing wrong. In this Example x should be equal to ones.
The goal is, to use it for a big matrix and calculate all unknown 'x'. If it is not possible to calculate them, I have to estimate the missing x, and solve it with something like a Netwon-Raphson method. But that will propably be in a later question.
Thank you for answering.
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Accepted Answer
Jon
on 19 Feb 2020
Edited: Jon
on 19 Feb 2020
It looks like you want to find all of the vectors satisfying Ax = 0 for some singular matrix , A. If so, you can do this using
X = null(A)
This returns a basis for the null space of a matrix A.
In your case MATLAB returns X = [0.5;0.5;0.5;0.5], any multiple of this will satisfy your equation,
so for example 2*[0.5;0.5;0.5,0.5] = [1;1;1;1] is a solution and you can verify that A*[1;1;1;1]=0
To find out more about the null function type doc null on the command line in MATLAB
7 Comments
Jon
on 20 Feb 2020
Edited: Jon
on 20 Feb 2020
Good catch!
Glad it seem like this approach will help you. One benefit of the least squares minimization, is that it very naturally handles the situation where you have sensor measurements of the flows but they may be noisy/slightly in error. Imagine that you in fact have all of the flows measured with noisy measurements. The measured flows will not satisfy Ax = 0 but you can find a set of flows which are as close as possible to the measured values (in the least square sense) but that satisfy Ax = 0. This is in some sense best physically consistent estimate of the overall network flows.
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