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3 cards from this section. Quick, good the night before a test.
What is a linear combination of the vectors (2, 3) and (1, -1)?
Try substituting different values for a and b.
Define the span of the set S = {(1, 2), (2, 3)}.
Think about how many combinations can be formed.
What is a linear combination of two vectors?
Think about how we create new vectors from existing ones.
The span of a set of vectors is always:
Remember the definition of span and its properties.
Let v₁ = (2, 3) and v₂ = (4, 6). Demonstrate whether these vectors are linearly independent or dependent by showing a linear combination.
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.
Think about how the bases span the entire axis.
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