Practice Definition Of Linear Independence (23.3) - Linear Independence

Practice: Definition of Linear Independence

Lesson 23.3Linear Independence

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Are the vectors [1, 0] and [0, 1] in R² linearly independent?
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Consider their geometric representation.
Question 2.
Determine if the vectors [1, 1] and [1, 2] are linearly independent.
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Look for a solution for coefficients that results in zero.
3Question 3.
What does it mean for a set of vectors to be linearly independent?
- They span the same space.
- They can be combined to give zero with non-zero solutions.
- Their linear combination results in zero only with all coefficients being zero.
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Recall the definition given in class.
4Question 4.
Is the set containing the zero vector linearly dependent?
- True
- False
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Consider the implications of the zero vector.
Question 5.
Prove that the vectors (1, 1, 1), (2, 2, 2), (3, 3, 3) are linearly dependent by showing how one vector is a linear combination of the others.
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Set up the equation and solve using coefficient comparison.
Question 6.
Given vectors (1, 0) and (a, b) in R², find conditions on a and b for independence.
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Use the determinant condition for independence.

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