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2 cards from this section. Quick, good the night before a test.
Determine if the following vectors are linearly dependent: (2,4), (1,2), (3,6)
Look for scalar multiples.
Are the vectors (1, 1) and (1, -1) linearly independent?
Set up the equation and solve.
What defines linear dependence among vectors?
Think in terms of solutions to linear equations.
True or False: If only linear combinations of zeros result in the zero vector, the vectors are linearly independent.
Recall the definitions of dependence versus independence.
In 3D space, consider vectors A = (1, 0, 0), B = (0, 1, 0), and C = (0, 0, 1). Are these vectors dependent or independent? Justify your answer with a general linear combination.
Use the definition of independence for validation.
Given the vectors D = (1, 2, 3), E = (2, 4, 6), and F = (1, 1, 1), determine if the set is dependent or independent and explain.
Check for scalar multiples and linear combinations.
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