Practice Rank Of A Matrix (22) - Rank of a Matrix - Mathematics (Civil Engineering -1)

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9 questions

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6 sample questions

Question 1.
What is the rank of the following matrix: [1 0; 0 1]?
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Count the independent rows.
Question 2.
Is the rank of a zero matrix always zero?
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Think about how many elements are non-zero.
3Question 3.
What is the maximum rank of a 4x2 matrix?
- 2
- 4
- 0
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Think about the number of columns.
4Question 4.
True or False: The rank of a diagonal matrix is equal to the number of non-zero elements on its diagonal.
- True
- False
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Remember the properties of diagonal matrices.
Question 5.
Given the matrix A = [4 2 1; 2 6 2; 6 4 0], calculate the rank using both the method of row reduction and determinants of minors.
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Use row operations and then check smaller square matrices.
Question 6.
Can you provide a matrix with rank 1 and explain why it is so?
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Check if one row can be generated from another.

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