📄 sy14.mht
字号:
30340;有理基。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>结果如下:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>C =3D</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'>
</span>2<span
style=3D'mso-spacerun:yes'> =
</span>5/3<span style=3D'mso-spacerun:yes'> </span>=
</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:23.1=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'>
</span>-2<span
style=3D'mso-spacerun:yes'> =
</span>-4/3<span style=3D'mso-spacerun:yes'> </span=
></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'>
</span>1<span
style=3D'mso-spacerun:yes'> =
</span>0<span style=3D'mso-spacerun:yes'> </s=
pan></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'>
</span>0<span
style=3D'mso-spacerun:yes'> =
</span>1</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>接着,用命令:</span=
></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>syms k1 k2</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>X=3Dk1*C(:,1)+k2*C(:,2)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>求出的通解为:</span=
></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>X =3D</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>[<span style=3D'mso-spacerun:yes'> </span>2*k1+5/3*k2]</=
span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>[ -2*k1-4/3*k2]</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>[<span
style=3D'mso-spacerun:yes'> =
</span>k1]</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>[<span
style=3D'mso-spacerun:yes'> =
</span>k2]</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>例</span><span
lang=3DEN-US>5</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>:求方程&#=
32452;</span><span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1029" type=3D"#=
_x0000_t75"
style=3D'width:119.25pt;height:56.25pt' o:ole=3D"">
<v:imagedata src=3D"sy14.files/image009.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D159 height=3D75
src=3D"sy14.files/image010.gif" v:shapes=3D"_x0000_i1029"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
029"
DrawAspect=3D"Content" ObjectID=3D"_1236256089">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的通=
解的程序为:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>clear</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>format rat</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>A=3Dsym('[1,2,2,1;2,1,-2,-2;1,-1,-4,-3]')</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>b=3Dsym('[1;2;2]')</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>B=3D[A,b]</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>n=3Dlength(b)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>RA=3Drank(eval(A))</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>RB=3Drank(eval(B))</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>if(RA=3D=3DRB&RA=3D=3Dn)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'> </span>X=3Deval(A\B)<s=
pan
style=3D'mso-spacerun:yes'> =
&nb=
sp;
</span><span style=3D'mso-spacerun:yes'> </span></span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>%在方程组满秩=
时,求出唯一解</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>elseif(RA=3D=3DRB&RA<n)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'> </span>C=
=3Deval(A\b)<span
style=3D'mso-spacerun:yes'> =
</span></span><span style=3D'font-family:SimSun;mso-ascii-font-family:"Time=
s New Roman";
mso-hansi-font-family:"Times New Roman"'>%在方程&#=
32452;不满秩时,求出特Š=
99;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'>
</span>D=3Dnull(eval(A),'r')<span
style=3D'mso-spacerun:yes'> </span></span><sp=
an
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>%求出矩阵</span><span
lang=3DEN-US>A</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>的零空间&#=
30340;基,即方程组的基ij=
84;解系</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'> </span>sym=
s k1 k2</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'>
</span>X=3Dk1*D(:,1)+k2*D(:,2)+C<span style=3D'mso-spacerun:yes'> &nbs=
p;
</span></span><span style=3D'font-family:SimSun;mso-ascii-font-family:"Time=
s New Roman";
mso-hansi-font-family:"Times New Roman"'>%求出方&#=
31243;组的全部解</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>else</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'> </span>fpr=
intf('No
Solution for the Equations')</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>end</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>结果请大家自己๡=
6;行。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>现在我们转而来=
看非线性方程组的求=
5299;,对于非线性方程ಭ=
2;,我们用函数</span><span
lang=3DEN-US>fsolve</span><span style=3D'font-family:SimSun;mso-ascii-font-=
family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>来求=
解。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>例</span><span
lang=3DEN-US>6</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>:求解非&#=
32447;性方程组</span><span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1030" type=3D"#=
_x0000_t75"
style=3D'width:144.75pt;height:38.25pt' o:ole=3D"">
<v:imagedata src=3D"sy14.files/image011.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D193 height=3D51
src=3D"sy14.files/image012.gif" v:shapes=3D"_x0000_i1030"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
030"
DrawAspect=3D"Content" ObjectID=3D"_1236256090">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>时,=
我们采用如下的方法=
5292;先建立存放函数的</span=
><span
lang=3DEN-US>m</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>文件,文&#=
20214;名必须与函数名一Ō=
68;,这里就应该为</span><span
lang=3DEN-US>sy6_6.m</span><span style=3D'font-family:SimSun;mso-ascii-font=
-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,内=
容如下:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt'><span
lang=3DEN-US>function y=3Dsy6_6(x)<span
style=3D'mso-spacerun:yes'> =
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