Q85.Let ๐ be any 3 ร 3 matrix with entries from the set 0, 1, 2. The maximum number of such matrices, for which the sum of diagonal elements of ๐๐๐ is seven, is______.
What This Question Tests
This question tests the understanding of matrix transpose and multiplication to derive the sum of diagonal elements, which simplifies to the sum of squares of all matrix entries. It then requires combinatorial analysis to count possible matrices whose entries (from {0,1,2}) sum up to 7 when squared.
Concepts Tested
Formulas Used
(M^T M)_{ii} = \sum_{k=1}^{3} (M_{ki})^2
Trace(M^T M) = \sum_{i=1}^{3} \sum_{k=1}^{3} (M_{ki})^2
๐ NCERT Sections This Tests
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๐ Question Details
- Chapter
- Matrices
- Topic
- Matrix multiplication and properties
- Year
- 2021
- Shift
- 24 Feb Shift 1
- Q Number
- Q85
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices
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