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October 22nd, 2015, 03:06 PM   #1
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matrix projection

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) 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.
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October 26th, 2015, 04:22 PM   #2
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So you have a matrix of the form where a, b, c, and d are unknown but you do know P= a+ b, Q= c+ d, the sums of the rows and R= a+ c, S= b+ d, the sums of the columns. That gives four equations to solve for the four values a, b, c, and d. Looks to me like it should be possible. What do you get when you try to solve those equations?
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