MHB Solving 2x2 Matrix Projection Problem: Strang's Approach

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Many important techniques in fields such as CT and MR imaging in medicine,
nondestructive testing and scientific visualization are based on trying
to recover a matrix from its projections. A small version of the problem
is given the sums of the rows and columns of a 2 x 2 matrix, determine the
elements of the matrix. Solve this problem or show why it cannot be solved(Strang)

 

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Many important techniques in fields such as CT and MR imaging in medicine,
nondestructive testing and scientific visualization are based on trying
to recover a matrix from its projections. A small version of the problem
is given the sums of the rows and columns of a 2 x 2 matrix, determine the
elements of the matrix. Solve this problem or show why it cannot be solved(Strang)

What have you tried so far? Have you looked at both possible outcomes? In other words, have you tried (a) to prove the result, and (b) to find a counterexample? A possible counterexample might consist of two different matrices with the same row sums and column sums.