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2 cards from this section. Quick, good the night before a test.
Determine whether the vectors (1, 1) and (2, 2) are linearly dependent.
Look for scalar multiples.
Are the vectors (1, 0) and (0, 1) linearly independent?
Check if one can be created through the other.
What does it mean for vectors to be linearly dependent?
Think of how many directions they actually span.
True or False: A set of vectors can be both linearly dependent and independent at the same time.
Consider the definitions.
Given vectors v₁ = (1, 1, 1), v₂ = (2, 2, 2), and v₃ = (3, 3, 3), prove whether they are dependent or independent.
Look for scalar relationships.
Using the vectors u = (1, 2, 3), v = (4, 5, 6), and w = (7, 8, 9), find the conditions under which these can be independent.
Matrix properties indicate independence.
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