Practice Maximal Linearly Independent Sets (23.14)

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6 sample questions

Question 1.
What defines a maximal linearly independent set?
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Think about what happens when you add a dependent vector.
Question 2.
What are pivot columns in a matrix?
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Consider where you see the first 1 in each row.
3Question 3.
What is a maximal linearly independent set?
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Reflect on the definition of independence.
4Question 4.
True or False: A maximal independent set can include a dependent vector.
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Remember the conditions of linear independence.
Question 5.
Given vectors (1,2,1), (2,4,3), and (3,3,1), find the maximal linearly independent set and explain your method.
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Consider how each column contributes to the total span.
Question 6.
How would you apply the concept of maximal independent sets in a network of sensors? Discuss both potential benefits and pitfalls.
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Focus on function versus redundancy.

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