QJEEAdv17Maaa00: JEE Advanced 2017 Mathematics - Class 12 JEEAdv17Maaa00 Solution: How many 3 3 matrices M with entries from {0, 1, 2} are there,…

Question

Verified Solution • 2025–26 Session moderate

How many 3

\times

3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of M^TM is 5?

Accepted Answer

Sum of diagonal entries of M^TM is

\sum\limits_{}^{} {a_i^2}

\sum\limits_{i = 1}^9 {a_i^2} = 5

Possibilities

I. 2, 1, 0, 0, 0, 0, 0, 0, 0, which gives

{{9!} \over {7!}}

matrices

II. 1, 1, 1, 1, 1, 0, 0, 0, 0, which gives

{{9!} \over {4!\, \times 5!}}

matrices

Total matrices = 9

\times

8 + 9

\times

7

\times

2 = 198

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