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4 cards from this section. Quick, good the night before a test.
Determine if the set { [1, 0], [0, 1], [1, 1] } is linearly independent.
Look for combinations of vectors that produce another vector in the set.
Is the set { [0, 0], [1, 1] } linearly independent?
Remember the importance of the zero vector.
A set containing the zero vector is linearly dependent.
Consider what the zero vector represents in a linear combination.
In R^4, a set of five vectors must be linearly independent.
Reflect on the dimensionality of R^n.
Prove that the three vectors v1 = (1,0,0), v2 = (0,1,0), v3 = (0,0,1) are linearly independent.
You can set up a matrix and check its rank or use geometric reasoning.
Consider the vectors u1 = (1,1,0), u2 = (2,2,0), u3 = (0,3,0). Are these vectors linearly independent? Justify your answer.
Check if any vector is a linear combination of the others.
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