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2 cards from this section. Quick, good the night before a test.
Are the vectors (1,2) and (2,4) linearly independent?
Check if one can be expressed as a multiple of the other.
Is the set of vectors (3, 1) and (1, -4) linearly independent?
Consider their direction in the 2D plane.
Two vectors are linearly independent if they are:
Think about their direction in the plane.
In R³, three vectors are linearly independent when they are:
Consider the relationship of three planes.
Prove whether the following set of vectors: (2, 3), (4, 6), and (1, 1) is linearly independent or dependent.
Use the definition of linear independence to check combinations.
Design an example of three vectors in R³ which are linearly independent and explain why.
Check their arrangement in space.
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