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Aug 14, 2016 at 15:37 comment added Mark L. Stone Letting M be a 1 by 2 matrix, such as [1 2], is sufficient to get an $\infty$ of solutions A, in accordance with comment ot the question by @Igor Khavkine .
Aug 14, 2016 at 15:20 history edited Mark L. Stone CC BY-SA 3.0
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Aug 14, 2016 at 15:16 comment added Mark L. Stone Here is the solution which maximizes trace(A) subject to the 2-norm of A being <= 100. A=[17.5 -33 16.5;-33 67 -33;16.5 -33 17.5]. I just "made up" this criterion, just as a way of selecting another of the $\infty$ of solution. I found this as a solution of a senidefinite optimization problem.
Aug 14, 2016 at 15:10 comment added Mark L. Stone It's s solution to an underdetermined set of linear equations. There are an $\infty$ number of solutions A with this M.
Aug 14, 2016 at 15:07 history edited Mark L. Stone CC BY-SA 3.0
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Aug 14, 2016 at 15:07 comment added Ulderique Demoitre Thanks, and how have you found $A$? Is there a general result that allows to find the solutions?
Aug 14, 2016 at 15:05 history answered Mark L. Stone CC BY-SA 3.0