Practice Rank Of Special Matrices (22.5) - Rank of a Matrix

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9 questions

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6 sample questions

Question 1.
What is the rank of a zero matrix of size 4x4?
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Think about how many independent rows there are.
Question 2.
What is the rank of the identity matrix of size 3?
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Recall the definition of an identity matrix.
3Question 3.
What is the rank of a zero matrix?
- 0
- 1
- n
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Remember what elements make up a zero matrix.
4Question 4.
True or False: The rank of an identity matrix is always less than its order.
- True
- False
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Consider the properties of identity matrices.
Question 5.
Given a diagonal matrix D = [0 0 7; 0 8 0; 9 0 0], determine its rank and explain why.
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Count all non-zero values on the diagonal.
Question 6.
For an upper triangular matrix U = [3 5 0; 0 0 0; 1 4 0], calculate the rank and justify your reasoning.
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Only consider rows that have at least one non-zero element.

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