title=Matrices multiplicadas por la izquierda
language=es
author=XIAO, Gang
email=xiao@unice.fr
format=html

!if $status=waiting
 !exit
!endif

type=matrix
cols=!item $qcmlevel of 2,3,2,3,2,3,4
rows=!item $qcmlevel of 2,2,3,3,3,3,3
row2=!item $qcmlevel of 1,1,1,1,2,2,2
col2=$rows
dim=$[$cols*$rows]
:redo
raw_matrix=
start=0
!for i=1 to $row2
 l=
 !for j=1 to $col2
  c=!randint -10,10
  !if $c!=0
   start=1
  !endif
  a$i$j=$c
  l=!append item $c to $l
 !next j
 raw_matrix=!append line $l to $raw_matrix
!next i
!if $start=0
 !goto redo
!endif

eqn=$[$row2*$cols]
zero=0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
!for i=1 to $row2
 !for j=1 to $cols
  ll=$zero
  !for k=1 to $rows
   ll=!replace item number ($k-1)*$cols+$j  by $(a$i$k) in $ll
  !next k
  eq$[$j+($i-1)*$cols]=!item 1 to $dim of $ll
 !next j
!next i

matrix_name=$m_B
!read mkmatrix
question=Sea $m_M<sub>$rows&times;$cols</sub> \
el espacio vectorial de las matrices $rows&times;$cols \
($rows filas and $cols columnas) y sea\
$m_S el subespacio de $m_M<sub>$rows&times;$cols</sub> definido por\
las matrices $m_A tales que $m_B$m_A=0, donde\
<center>$html_matrix</center> <p>\
Encontrar una base de $m_S.

