Practice Rank Of A Matrix (21.5) - Linear Algebra - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
What is the rank of a matrix with all zero rows?
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Think about the definition of linearly independent vectors.
Question 2.
If a matrix has 3 rows and 2 linearly independent rows, what is its rank?
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Remember, rank corresponds to independent rows.
3Question 3.
What is the rank of a matrix?
- Number of rows
- Number of columns
- Maximum number of linearly independent vectors
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Focus on the meaning of independence in vectors.
4Question 4.
True or False: A matrix with more rows than columns can always have rank equal to the number of rows.
- True
- False
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Consider the relationship of linear dependence.
Question 5.
Given the matrix A = [[2, 4, 1], [6, 10, 3], [4, 8, 2]], find its rank by row-reduction and explain your steps.
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Focus on identifying dependent rows.
Question 6.
Demonstrate the impact of rank on the solutions of the linear system represented by A. If rank(A) < rank([A | b]), what can you conclude?
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Think about the augmentation of the matrix and about linear equations.

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