前言:
眼前你们对“n元线性方程组n指的是行还是列”大概比较关心,兄弟们都想要学习一些“n元线性方程组n指的是行还是列”的相关资讯。那么小编在网摘上汇集了一些对于“n元线性方程组n指的是行还是列””的相关资讯,希望我们能喜欢,同学们一起来学习一下吧!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 EDITgui_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});endif 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 jisuanfangchengzuhandles.output = hObject;movegui(gcf,'center');% Update handles structureguidata(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 structurevarargout{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');endfunction 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');endfunction 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)) end
3.参考内容
[1] CSDN博主MicroSmiles的文章《线性方程组求解》,文章链接:
[2] 百度词条.
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作 者 | 郭志龙
编 辑 | 郭志龙
校 对 | 郭志龙
标签: #n元线性方程组n指的是行还是列