SOLUTION: Entries of a 2*2 determinant are chosen from the set (-1,1).The probability that determinant has zero value is ?

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Question 1094961: Entries of a 2*2 determinant are chosen from the set (-1,1).The probability that determinant has zero value is ?
Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
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The number of 2x2 matrices comprised of numbers +/-1 in each entry/position is 2%5E4 = 16.


Of them, exactly 8 matrices


%28matrix%282%2C2%2C+1%2C1%2C+1%2C1%29%29,  %28matrix%282%2C2%2C+1%2C-1%2C+1%2C-1%29%29,  %28matrix%282%2C2%2C+-1%2C1%2C+-1%2C1%29%29,  %28matrix%282%2C2%2C+-1%2C-1%2C+-1%2C-1%29%29,   %28matrix%282%2C2%2C+1%2C1%2C+-1%2C-1%29%29,  %28matrix%282%2C2%2C+-1%2C-1%2C+1%2C1%29%29,  %28matrix%282%2C2%2C+1%2C-1%2C+-1%2C1%29%29  and   %28matrix%282%2C2%2C+-1%2C1%2C+1%2C-1%29%29


with identical or proportional rows have the determinant equal to zero.



So, the probability under the question is 8%2F16 = 1%2F2.

Solved.