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What is the total number of 3 × 3 matrices M, whose elements are chosen from {0, 1, 2}, such that the sum of the diagonal elements of MᵀM equals 5?
- 62
- 198
- 126
- 135
Correct answer: 198
Solution
The total number of 3 × 3 matrices M with elements chosen from {0, 1, 2} such that the sum of the diagonal elements of MᵀM equals 5 can be found by considering the possible combinations of elements that satisfy the given condition, resulting in 198 such matrices.
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