Practice Exercises (23.10) - Linear Independence - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Determine if the set of vectors { (1,0), (0,1) } is linearly independent.
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Consider their geometric representation.
Question 2.
Is the vector { (1,1), (1,1) } linearly independent?
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Look for redundancy in vectors.
3Question 3.
True or False: A set of vectors is linearly independent if at least one vector can be expressed as a combination of others.
- True
- False
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Recall the definitions of independence and dependence.
4Question 4.
Which of the following sets of vectors are linearly dependent? {(1,0),(1,0)}, {(1,2),(2,4)}, or {(1,1),(1,-1)}?
- Set A
- Set B
- Set C
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Look for vectors that can be expressed in terms of each other.
Question 5.
Given the vectors {(1,2,3), (2,4,6), (3,6,9)}, demonstrate through matrix methods that they are dependent.
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Look at the ratios between the rows.
Question 6.
In R^3, provide a set of four vectors and argue whether they can be independent or dependent.
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Recall dimensional limits in linear algebra.

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