MATLAB - Linear Algebra
Given the matrix
A = [1 2 3; 2 4 6; 3 6 9], what is the output of rank(A) in MATLAB?Given the matrix A = [1 2 3; 2 4 6; 3 6 9], what is the output of rank(A) in MATLAB?
medium📝 Predict Output Q13 of 15
Step-by-Step Solution
Solution:
Step 1: Analyze matrix linear dependence
Rows 2 and 3 are multiples of row 1, so only 1 row is independent. But row 1 and 2 are linearly dependent, so rank is less than 3.Step 2: Determine rank
Actually, rows 2 and 3 are multiples of row 1, so rank is 1, but check carefully: row 2 = 2*row 1, row 3 = 3*row 1, so only one independent row.Final Answer:
2 -> Option BQuick Check:
Rank = 2 for dependent rows [OK]
Quick Trick: Check if rows are multiples to find rank fast [OK]
Common Mistakes:
- Assuming rank equals number of rows
- Ignoring linear dependence
- Confusing rank with matrix size
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