(* Require XMLgen_MC.nb ver >=0.24 *)
SetDirectory[NotebookDirectory[]];
<<XMLgenMC.mx;
DebugMode=False;
ThisNo=StringReplace[StringSplit[ NotebookFileName[],"/"][[-1]],{"LA_"->"",".nb"->"","_"->"-"}];
Category="LA/"<>ThisNo<>".";

(* Global Options *)
Numbering="abc";Title="3次行列式の性質(総合)";
(* Numbers of select options and questions *)
Shuffle="true";Single="true";SELNUM=8;NUM=300;
GeneralFeedback="";

TOT[mt_]:=ToString[OneLineTeXForm[mt]];
TOTT[mt_]:=ToString[OneLineTeXForm[Transpose[mt]]];
TTSt[eq_]:=ToString[TeXForm[StandardForm[eq]]];
TOC[mt_,c_]:=TOTT[{Transpose[mt][[c]]}];
TTD[r_]:=StringReplace[TT[r],"\\frac"->"\\dfrac"];
MFT[m_]:=MatrixForm[Transpose[m]];
MF[m_]:=MatrixForm[m];
Rnz[m_]:=(RandomInteger[m]+1)*(2*RandomInteger[1]-1); (* \\pm 1,\pm2,...,\pm(m+1) *)
Rpos[m_]:=RandomInteger[m]+1; (* 1,2,...,m+1 *)
Rbtw[m_]:=RandomInteger[2m]-m;
TTC[A_,n_]:=TOTT[{(Transpose[A])[[n]]}];
PtString[M_]:=StringReplace[ToString[M],{"{"->"(","}"->")"}];
ai2tex[s_]:=StringReplace[TOT[s],Table["\\text{a"<>TOT[i]<>"}"->"{\\mathbf a}_"<>TOT[i],{i,1,8}]];
ci2tex[c_,s_]:=StringReplace[s,Table["\\text{"<>c<>TOT[i]<>"}"->"{\\mathbf "<>c<>"}_"<>TOT[i],{i,1,5}]];
ci2tex[c_,s_,tx_]:=StringReplace[s,Table["\\text{"<>c<>TOT[i]<>"}"->"{"<>tx<>c<>"}_"<>TOT[i],{i,1,8}]];
TOTci2tex[c_,s_]:=StringReplace[TOT[s],Table["\\text{"<>c<>TOT[i]<>"}"->"{\\mathbf "<>c<>"}_"<>TOT[i],{i,1,8}]];
TeXArray2Matrix[s_,mtx_]:=StringReplace[s,Join[{"array"->mtx,"\\left("->"","\\right)"->""},#->"" &/@ ("{"<>StringRepeat["c",#]<>"}" &/@ Reverse[Range[20]])]];
TAM[s_,mtx_]:=TeXArray2Matrix[TOT[s],mtx];
TpStr[L_]:="\\("<>TOT[L[[1]]]<>"\\times"<>TOT[L[[2]]]<>"\\)";
TpTpse[L_]:=If[L=={},{},{L[[2]],L[[1]]}];
PType[A_,B_]:=If[A=={}||B=={},Return[{}],
If[A[[2]]===B[[1]],Return[{A[[1]],B[[2]]}],Return[{}]]];
PTypeL[L_]:=Module[{ct,len,tmp},len=Length[L];
Which[len==0,Return[{}],len==1,Return[L[[1]]],
len==2,Return[PType[L[[1]],L[[2]]]],
True,tmp=L[[1]];For[ct=2,ct≤len,ct++,tmp=PType[tmp,L[[ct]]]];Return[tmp]]];
GCDL[L_]:=Module[{ct,ret=0},For[ct=1,ct≤Length[L],ct++,ret=GCD[ret,L[[ct]]]];Return[ret]];

Clear[p,q,r,s,t,u,v,x,y,z]

(* select pairs of matrices *)
MAList=Range[-9,9];sz=3;
QtList={}; For[ct=1,ct≤NUM*1.02,ct++,
Cn=RandomChoice[{2,2,2,3,3,3,3,4,4}]; (* 1/8 *)
While[Det[MA=ArrayReshape[RandomSample[MAList,sz*sz],{sz,sz}]]==0];
QtList=Append[QtList,{Cn,sz,MA}]];
(* QtList=DeleteDuplicates[QtList]; *)
QtList=RandomSample[QtList,NUM];Length[QtList]

Clear[a,b,c,QtextF];QtextF[mm_]:=Module[{Cn,sz,MA,ret,ct},
{Cn,sz,MA}=QtList[[mm]];
ret="行列式は列や行に重複(同じもの)があると\\(0\\)になるという退化性を持っている."
<>"今, \\("<>TOT[MA]<>"\\)の行列式は\\(0\\)ではない."
<>"以下の\\("<>TOT[sz]<>"\\)次行列式のうち, \(0\)になるものを<u>1つ</u>選びなさい."
<>"(複数ある場合もあるが1つ選べばよい).";
Return[IfDeb[{MF[MA]},ret]]];

AListF[mm_]:=Module[{Cn,sz,MA,MA1,Prm,Rg,i,j,ct,CL={},IL={},fsL={},ret={}},
{Cn,sz,MA}=QtList[[mm]];Rg=Range[sz];
Prm=Permutations[Rg,{2}];
For[ct=1,ct≤Length[Prm],ct++,{i,j}=Prm[[ct]];
MA1=MA;MA1[[j]]=MA[[i]]*Rnz[2];CL=Append[CL,MA1];
MA1=MA;MA1[[Range[sz],j]]=MA[[Range[sz],i]]*Rnz[2];
CL=Append[CL,MA1]];
For[ct=1,ct≤Length[Prm],ct++,{i,j}=Prm[[ct]];
MA1=MA;MA1[[j]]=MA[[i]];MA1[[i]]=MA[[j]];IL=Append[IL,MA1];
MA1=MA;MA1[[Rg,j]]=MA[[Rg,i]];MA1[[Rg,i]]=MA[[Rg,j]];IL=Append[IL,MA1]];
CL=RandomSample[DeleteDuplicates[CL],Cn];
IL=RandomSample[DeleteDuplicates[IL],SELNUM-Cn];
fsL=Append[fsL,"正解です."];fsL=Append[fsL,"違います. \\(0\\)にはなりません."];
For[ct=1,ct≤Length[CL],ct++,
ret=Append[ret,{"C",IfDeb[MF[CL[[ct]]],"\\("<>TAM[CL[[ct]],"vmatrix"]<>"\\)"],fsL[[1]]}]];
For[ct=1,ct≤Length[IL],ct++,
ret=Append[ret,{"I",IfDeb[MF[IL[[ct]]],"\\("<>TAM[IL[[ct]],"vmatirx"]<>"\\)"],fsL[[2]]}]];
ret=RandomSample[ret];Return[Join[{{Cn,SELNUM-Cn}},ret]]];

QtextF[3]

DebOn[];AListF[3]

DebOn[];For[ct=1,ct≤NUM,ct++,PrintTemporary[ct];QtextF[ct];AListF[ct]]

(* For[ct=1,ct≤NUM,ct++,Print[ct];QtextF[ct];AListF[ct]]; (* Error Check *) *)

DebOff[];GenMCxmlV2[DFname[1],Category<>Title<>"(MC1)",Title,NUM,Single,QtextF,AListF]

Tmp={{a,b,c},{d,e,f},{g,h,i}}

Tmp1=Tmp;
Tmp1[[Range[1,3],2]]=Tmp[[Range[1,3],3]]*2;

Tmp1