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row sums

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Odds and evens in an n by n+1 table 2010-01-21
Shankar pose la question :
The boxes of an n * (n+1) table ( n rows and n+1 columns) are filled with integers. Prove that one can cross out several columns ( not all of them !) so that after this operation all the sums of the numbers in each row will be even.
Robert Dawson lui répond.
Two matrix problems 2005-03-30
Sue pose la question :
Question 1
Suppose all matrices in the equation below are square and invertible. Solve for x .

BA-1XB-1 + 2BA + In = 0 (the symbol "0" here denotes the matrix of all 0's in it)

Also, A-1 or B-1 is indicating inverse and "In" = for example, A-1 times A
I hope you understand the above. I have to show all the steps.

Question 2
Suppose we consider the set of all 2x2 matrices along with the operations of matrix addition and multiplication. Do they form a field? Why or why not?
I think the answer is no because under multiplication it is not commutative and not all square matrices are invertible. I not positive so I'd like some help.

Penny Nom lui répond.
A matrix construction problem 2005-03-14
Marcelo pose la question :
I want to know if is it possible to solve this problem:
I have an empty NxM matrix and I know totals (sum) by rows and totals by column.
Is there any algorithm to fill the matrix so that the summary of columns and rows gives the original values I have?

Harley Weston lui répond.
 
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