MATLAB - Linear Algebra
Given
B = [1 0 0; 0 1 0; 0 0 0], what is the dimension of the null space of B in MATLAB?Given B = [1 0 0; 0 1 0; 0 0 0], what is the dimension of the null space of B in MATLAB?
medium📝 Predict Output Q5 of 15
Step-by-Step Solution
Solution:
Step 1: Calculate rank of B
Matrix B has two independent rows, so rank(B) = 2.Step 2: Use dimension formula for null space
Nullity = number of columns - rank = 3 - 2 = 1.Final Answer:
1 -> Option AQuick Check:
Null space dimension = columns - rank = 1 [OK]
Quick Trick: Nullity = columns minus rank of matrix [OK]
Common Mistakes:
- Confusing null space dimension with rank
- Counting zero rows as rank
- Forgetting to subtract rank from columns
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