Practice Summary Table: Quick Tests For Linear Independence (23.17) - Linear Independence

Practice: Summary Table: Quick Tests for Linear Independence

Lesson 23.17Linear Independence

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8 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Determine if the vectors [1, 0] and [0, 1] are linearly independent.
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Check if you can form one vector from the other.
Question 2.
Using the Wronskian, test the independence of functions f(x) = e^x and g(x) = e^(2x).
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Calculate the determinant of the matrix formed by the functions and their derivatives.
3Question 3.
What is the criterion for vectors in Rn to be linearly independent?
- Row reduced matrix must have full rank
- Vectors must be orthogonal
- Vectors cannot be identical
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Think about what rank implies for the set of vectors.
4Question 4.
Is the Wronskian used for functions or vectors?
- True
- False
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Recall the definition of the Wronskian.
Question 5.
Given vectors v1 = [1, 2, 3], v2 = [2, 4, 6], and v3 = [1, 0, 1], determine if they form a basis for R3.
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Use row reduction to analyze their relationships.
Question 6.
For the functions f(x) = x and g(x) = x^2, calculate the Wronskian and describe their independence.
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Perform the determinant calculation for completeness.

4 more questions in this section. Enroll free to practise them all.