reserve x,y for set,
  i,j,k,l,m,n for Nat,
  K for Field,
  N for without_zero finite Subset of NAT,
  a,b for Element of K,
  A,B,B1,B2,X,X1,X2 for (Matrix of K),
  A9 for (Matrix of m,n,K),
  B9 for (Matrix of m,k,K);
reserve D for non empty set,
  bD for FinSequence of D,
  b,f,g for FinSequence of K,
  MD for Matrix of D;

theorem
  LineVec2Mx (k|->0.K) = 0.(K,1,k)
proof
  card(k|->0.K) = k by CARD_1:def 7;
  then reconsider L=LineVec2Mx (k|->0.K) as Matrix of 1,k,K;
  set Z=0.(K,1,k);
  now
A1: width L=k by MATRIX_0:23;
A2: dom L = Seg len L & len L=1 by FINSEQ_1:def 3,MATRIX_0:def 2;
    let i,j such that
A3: [i,j] in Indices L;
A4: j in Seg width L by A3,ZFMISC_1:87;
    i in dom L by A3,ZFMISC_1:87;
    then
A5: i=1 by A2,FINSEQ_1:2,TARSKI:def 1;
    Indices Z=Indices L by MATRIX_0:26;
    hence Z*(i,j) = 0.K by A3,MATRIX_3:1
      .= (k|->0.K).j by A4,A1,FINSEQ_2:57
      .= Line(L,i).j by A5,Th25
      .= L*(i,j) by A4,MATRIX_0:def 7;
  end;
  hence thesis by MATRIX_0:27;
end;
