Q74.The number of all 3 × 3 matrices A, with entries from the set {−1, 0, 1} such that the sum of the diagonal elements of AAT is 3, is ___________.
What This Question Tests
This problem requires understanding matrix multiplication, particularly the diagonal elements of AAᵀ, and then using combinatorial reasoning to count matrices with entries from a specific set that satisfy the given trace condition.
Concepts Tested
Formulas Used
Trace(A) = ΣAᵢᵢ
(AAᵀ)ᵢᵢ = Σₖ AᵢₖAᵀₖᵢ = Σₖ (Aᵢₖ)²
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📋 Question Details
- Chapter
- Matrices
- Topic
- Properties of matrices
- Year
- 2020
- Shift
- 08 Jan Shift 1
- Q Number
- Q74
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices
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