Discussion Forum

How many 3x3 matrices M with entries from {0,1,2} are there, for which the sum of the diagonal entries of M^TM is 5?

Answer:

Explanation:

Sum of diagonal entries of M^TM is Σ a₁²

          $\sum_1^9a_1^2=5$

Possibilities

I.  2,1,0,0,0,0,0,0,0 which gives $\frac{9!}{7!}$ matrices

II. 1,1,1,1,1,0,0,0,0 which gives $\frac{9!}{4!\times5!}$ matrices

Total matrices= $9\times8+9\times7\times2=198$