QQuestionMathematics
QuestionMathematics
If A is a 3×5 matrix, what are the possible values of nullity(A)?
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Recall the Rank-Nullity Theorem
\text{rank}(A) + \text{nullity}(A) = n
The Rank-Nullity Theorem states that for a matrix A with m rows and n columns:
Step 3:: Identify the matrix dimensions
- A is a 3×5 matrix - Number of columns (n) = 5 - Number of rows (m) = 3
Step 4:: Determine the maximum possible rank
\text{max rank} = \min(m, n) = \min(3, 5) = 3
The maximum possible rank is the minimum of the number of rows and columns
Step 5:: Calculate possible nullity values
- If rank = 3: $$5 - 3 = 2
Using the Rank-Nullity Theorem: Possible rank values: 0, 1, 2, 3 Corresponding nullity values:
Final Answer
2, 3, 4, 5
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