MATLAB线性方程组的求解及应用，非齐次线性方程组是数学方程组的一种，它符合以下的形式：
如果用线性代数中的概念来表达，则线性方程组可以写成：
Ax= b
这里的A是m×n 矩阵，x是含有n个元素列向量，b是含有m 个元素列向量。
齐次方程：AX=0
1. r(A)=未知数个数n（约束较强），该解空间只含有零向量。
2.r(A)<未知数个数n（约束不够），由齐次线性方程组解空间维数 = n - r(A) >0，所以该齐次线性方程组有非零解，而且不唯一，存在一个基础解系（基础解系中的向量个数为 n - r(A)个)。
非齐次方程：AX=B
（1）R(A)< r(A|B),方程组无解 。
（2）r(A)=r(A|B)=n,方程组有唯一解 。
（3）r(A)=r(A|B) < n,方程组有无穷解 。
（4）r(A)>r(A|B),这种情况不存在 。
其中r()代表矩阵的秩，A|B是增广矩阵，n是X未知数个数。
1.MATLAB求解线性方程组的GUI界面
Step1:输入齐次方程组Ax=0的系数矩阵A。
Step2：点击计算齐次按键，判断方程组求解结果情况，有解时计算出基础解系。
Step3:输入非齐次方程组Ax=b的系数矩阵A和增广矩阵b。
Step4：点击计算非齐次按键，判断方程组求解结果情况，有解时计算出基础解系和特解，有唯一解时求出对应的唯一解。
Step5:点击清除按键，清除输入。
Step6: 点击关闭。
2.程序
下面呈现主要程序，需要完整程序的可以赞赏20元及以上，进行联系，或者发截图到微信公众号云龙派对话窗口或者直接在公众号里，点击“联系掌门”按键，编程不易，还请见谅。
function varargout = jisuanfangchengzu(varargin)
% JISUANFANGCHENGZU MATLAB code for jisuanfangchengzu.fig
% JISUANFANGCHENGZU, by itself, creates a new JISUANFANGCHENGZU or raises the existing
% singleton*.
%
% H = JISUANFANGCHENGZU returns the handle to a new JISUANFANGCHENGZU or the handle to
% the existing singleton*.
%
% JISUANFANGCHENGZU('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in JISUANFANGCHENGZU.M with the given input arguments.
%
% JISUANFANGCHENGZU('Property','Value',...) creates a new JISUANFANGCHENGZU or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before jisuanfangchengzu_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to jisuanfangchengzu_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLE
% Edit the above text to modify the response to help jisuanfangchengzu
% Last Modified by GUIDE v2.5 21-Apr-2022 22:22:52
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @jisuanfangchengzu_OpeningFcn, ...
'gui_OutputFcn', @jisuanfangchengzu_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before jisuanfangchengzu is made visible.
function jisuanfangchengzu_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to jisuanfangchengzu (see VARARGIN)
% Choose default command line output for jisuanfangchengzu
handles.output = hObject;
movegui(gcf,'center');
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes jisuanfangchengzu wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = jisuanfangchengzu_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
function edit2_Callback(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit2 as text
% str2double(get(hObject,'String')) returns contents of edit2 as a double
% --- Executes during object creation, after setting all properties.
function edit2_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function edit3_Callback(hObject, eventdata, handles)
% hObject handle to edit3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit3 as text
% str2double(get(hObject,'String')) returns contents of edit3 as a double
% --- Executes during object creation, after setting all properties.
function edit3_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function edit1_Callback(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit1 as text
% str2double(get(hObject,'String')) returns contents of edit1 as a double
% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
A = str2num(get(handles.edit1,'string'));
Rank_A=rank(A);
[m,n]=size(A);
if(Rank_A<n)
%秩小于未知量的个数，方程组有无穷解
%计算基础解系1
set(handles.edit2,'string',"方程组有无穷解!")
z=null(A,'r');
set(handles.edit3,'string',num2str(z))
elseif(Rank_A==n)
set(handles.edit2,'string',"方程组只有零解!")
z=repmat(0,n,1);
set(handles.edit3,'string',num2str(z))
end3.参考内容
[1] CSDN博主MicroSmiles的文章《线性方程组求解》，文章链接：https://blog.csdn.net/weixin_39752599/article/details/103585651
[2] 百度词条.https://baike.sogou.com/v179854.htm?fromTitle=%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84&ch=frombaikevr
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作 者 | 郭志龙
编 辑 | 郭志龙
校 对 | 郭志龙