Other examples.

 

• LU decomposition example:
  

  

  LU2 returns:

  

  We have A=l^-1U.

• Rank of a matrix:
  

  

  hit RED RANG, and look at the matrix, the rank is the number of non zero lines (BTW you get a half reduced matrix)

• Linear relations between vectors
  Suppose we want to know the rank and linear relations existing between v₁(1,2,0), v₂(-2,-1,1), :

  { { 1 2 0 V1 }
    { -2 -1 1 V2 }
    { 0 3 1 V3 } }

  then RED, RANG, we get:

  { { 1 2 0 V1 }
    { 0 3 1 '2*V1+V2' }
    { 0 0 0 '-(2*V1)-V2+V3' } }

  The family is of rank 2 (the 3rd line is 0) and -2v₁-v₂+v₃=0.

 
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