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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a linear combination of the vectors (2, 3) and (1, -1)?
💡 Hint: Try substituting different values for a and b.
Question 2
Easy
Define the span of the set S = {(1, 2), (2, 3)}.
💡 Hint: Think about how many combinations can be formed.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a linear combination of two vectors?
- A vector formed by adding two vectors
- A vector formed by scaling and adding two vectors
- A vector formed only from one of the vectors
💡 Hint: Think about how we create new vectors from existing ones.
Question 2
The span of a set of vectors is always:
- True
- False
💡 Hint: Remember the definition of span and its properties.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Let v₁ = (2, 3) and v₂ = (4, 6). Demonstrate whether these vectors are linearly independent or dependent by showing a linear combination.
💡 Hint: Use the definition to write out the coefficients that lead to 0.
Question 2
Given a set of vectors {v₁, v₂, v₃} in R³, where v₁ = (1, 0, 0), v₂ = (0, 1, 0), v₃ = (0, 0, 1). Explain the significance of their span.
💡 Hint: Think about how the bases span the entire axis.
Challenge and get performance evaluation