Rank Of Matrix

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The rank of the matrix A = [[1, 2, 3], [2, 4, 6], [3, 6, 9]] is

RankGuru · Accepted Answer

1. **Definition of Rank**: Rank is the number of linearly independent rows (or columns) in a matrix.
2. **Row Dependence Check**:
   - Row 2 ($[2, 4, 6]$) is exactly $2 	imes$ Row 1 ($[1, 2, 3]$).
   - Row 3 ($[3, 6, 9]$) is exactly $3 	imes$ Row 1 ($[1, 2, 3]$).
3. **Independency**: Since both secondary rows are scalar multiples of the first, there is only **1** linearly independent row.
4. **Result**: The rank is 1.

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Rank Of Matrix

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