Question

How many matrixes (m*n) there are with 0 & 1 entries such that the number of 1s in every row and every column be an odd number.

Answer 1

*

Answer 2

I find out the solution I think...
Ummm... as an Idea we can think this way...
let have A[aij] (m-1 * n-1 ) any matrix with entries with o and 1. how many matrixes there are so..? any entry can be 1 or 0...
so we have 2^(m-1)(n-1) such matrixes.
now we add last row and column... but... if the number of 1s in m-1 entries in a row be odd we put last entry 0, else put it 1.
so last row and column will fill this way that will fulfill the situation... but this adding dont add any new case to our previous existing matrixes...
it is almost done... but there was some important points... adding 1 or 0 will not disturb the situation of rows and columns that have been made before.. IF : if m be odd then n be odd... or if m be even then n be even too.
the point I was doubting before i submit this,,.. was that is there any other matrixes that : m be odd and n be even or n be odd and m be even...
i dont have any proof for this but can say that such a matrix can't be found in these conditions.. ( rows and columns with odd number odd 1 )
so the number of such a matrixes is 2^(m-1)(n-1)...
I will be approciated for any better idea.
thanks :)

Answer 3

is the answer 13???

Answer 4

no... the answer depends on m and n... it is general case...
the answer is 2^( (m-1)(n-1))

Answer 5

ooh sorry i have done in case of 3x3 but i got 13
according to ur formula it should be 16

Answer 6

ya i got 16
u r right