algebra

How many 3 by 3 determinants can be formed whose value is always zero , using two non zero distinct elements say a and b ??? Please help !!!

Easy Math Editor

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Comments

You wanted to know how many determinants can be formed....see any two determinant can be said different whether its orientation of its terms are different....you are using only 2 non zero element ,you assumed "a" and "b"...now watch that in any place out of the 9 places of a 3 by 3 determinant you put them them and as a result you would get the result zero for every representation......so there are 9 places (3 rows 3 columns ) you are choosing 2 different places out of them .....you could do this in 9C2 ways....so there should (i'm not using "would" as i am not sure for my own logic and apprehension ) be only 36 ways to form different determinant....let's see if any one backs me up for this procedure to be right or wrong......

Sayan Chaudhuri - 8 years, 1 month ago

66 ways.