theorem Th75:
  for pf being FinSequence of R
  for N being Matrix of 3,R st
  len pf = 3 holds
  Line(N * (<*pf*>@),1) = <* (N * (<*pf*>@))*(1,1) *> &
  Line(N * (<*pf*>@),2) = <* (N * (<*pf*>@))*(2,1) *> &
  Line(N * (<*pf*>@),3) = <* (N * (<*pf*>@))*(3,1) *>
  proof
    let pf be FinSequence of R;
    let N be Matrix of 3,R;
    assume len pf = 3;
    then N * (<*pf*>@) is Matrix of 3,1,R by Th74;
    hence thesis by Th73;
  end;
