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Let M be any 3 × 3 matrix with entries from the set 0 , 1 , 2 . The maximum number of such matrices, for which the sum of diagonal elements of M T M is seven, is______.

Correct answer

0

Step-by-step solution

a b c d e f g h i a d g b e h c f i a 2 + b 2 + c 2 + d 2 + e 2 + f 2 + g 2 + h 2 + i 2 = 7 Case-I : Seven 1 ' s and two 0 ' s C 2 9 = 36 Case-II: One 2 and three 1 ' s and five 0 ' s 9 ! 5 ! 3 ! = 504 ∴ Total = 540

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