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Rectangular Matrix Product Poser (Posted on 2016-04-16) Difficulty: 4 of 5
Let A and B be the two matricies:
      [ 4  2 -10 ]       [ 0  3 ]
  A = [-1  1   5 ]   B = [-2  5 ]
      [-1 -2  -2 ]  
Find a 3x2 matrix C with rank 2 such that A*C = C*B.

See The Solution Submitted by Brian Smith    
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possible solution enlarged | Comment 2 of 4 |
I have revised again the question, and this time the matrix reductor (see my precedent post) gave a wider answer. 

It came out that the matrix C can be expressed as a linear combination of matricies:

[c11  c12]              [4   -6]             [-2  -4]     
[c21  c22]   =   m* [-2   3]    + n*   [ 3   0]
[c31  c32]              [0    0]             [-1   1]


For each value of m and n there is a valid solution. My last post solution is particular when m=0, n=-1. 
Other particular solution is for m=1 n=0. Then the matrix C has the last line in 0. 

The solution in this case is simple but both non-zero lines are dependents, so I suppose this means that this particular solution is not a rank 2 matrix. 

  Posted by armando on 2016-04-18 09:43:30
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