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How many 3 × 3 matrices M with entries from {0,1,2} are there, for which the sum of the diagonal entries of MTM is 5 ?
  • a)
    198
  • b)
    126
  • c)
    135
  • d)
    162
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
How many 3 × 3 matrices M with entries from {0,1,2} are there, f...
Let = 
∴ tr(MTM) = a2 + b2 + c2 + d2 + c2 + f+ g2 + h2 + i2 = 5,
where entries are {0,1,2} Only two cases are possible.
(I) five entries 1 and other four zero
9C5 × 1
(II) One entry is 2, one entry is 1 and others are 0.
9C2 × 2!
Total = 126 + 72 = 198.
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How many 3 × 3 matrices M with entries from {0,1,2} are there, for which the sum of the diagonal entries of MTM is 5 ?a)198b)126c)135d)162Correct answer is option 'A'. Can you explain this answer?
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