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.
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 nonzero lines are dependents, so I suppose this means that this particular solution is not a rank 2 matrix.

Posted by armando
on 20160418 09:43:30 