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 October 22nd, 2015, 03:06 PM #1 Newbie   Joined: Oct 2015 From: London Posts: 22 Thanks: 0 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.
 October 26th, 2015, 04:22 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 So you have a matrix of the form $\begin{bmatrix}a & b \\ c & d\end{bmatrix$ 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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