Rank Of Matrix
The rank of the matrix A = [[1, 2, 3], [2, 4, 6], [3, 6, 9]] is
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About This Question
- Subject
- mathematics
- Chapter
- matrices and determinants
- Topic
- rank of matrix
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
1
- Definition of Rank: Rank is the number of linearly independent rows (or columns) in a matrix.
- Row Dependence Check:
- Row 2 ([2,4,6]) is exactly 2× Row 1 ([1,2,3]).
- Row 3 ([3,6,9]) is exactly 3× Row 1 ([1,2,3]).
- Independency: Since both secondary rows are scalar multiples of the first, there is only 1 linearly independent row.
- Result: The rank is 1.
This medium difficulty mathematics question is from the chapter matrices and determinants, covering the topic of rank of matrix. It appeared in the 2025 exam.
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