Sun February 15, 2009 By:

if each element of a second order determinant is either 0 or 1 what is probability that value is

Expert Reply
Tue February 17, 2009

let the matrix entries be a,b,c,d

then total no. of matrices = 24 (for each entry we have two choices 0 or 1 )

determinant of the matrix = ad - bc

it wil be positive only if a and both are 1 and either or both of b or c is zero.

the no. of such matrices will be 3. (a=1,d=1 and (b=0,c=0) / (b=0,c=1) / (b=1,c=0) )

so desired probability = 3/16

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