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- Mar 12th 2009, 05:27 AMchamprockMatrices question
- Mar 13th 2009, 07:37 AMGrandadMatrices
Hello champrockThe answer is (c): every row and every column of contains just one , and zeros. Let me try and explain why.

Suppose the elements of are . In other words the element in row , column is . Suppose also that the elements of are , and the elements of are

Then

Now for each is formed when the elements of row of matrix are combined (by multiplication and addition) with the elements of . In other words:

And 's elements are a re-arrangement of 's elements. So for each for some . Therefore, from the above equation:

So each row of contains a single , and zeros. Moreover, each is equal to a different , so no column of contains more than a single . So is bistochastic, with elements and .

Grandad