26.4 - Linear Combination and Span
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Practice Questions
Test your understanding with targeted questions
What is a linear combination of the vectors (2, 3) and (1, -1)?
💡 Hint: Try substituting different values for a and b.
Define the span of the set S = {(1, 2), (2, 3)}.
💡 Hint: Think about how many combinations can be formed.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a linear combination of two vectors?
💡 Hint: Think about how we create new vectors from existing ones.
The span of a set of vectors is always:
💡 Hint: Remember the definition of span and its properties.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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