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3 cards from this section. Quick, good the night before a test.
Define the term 'rank' in the context of a matrix.
Think about linear independence.
What does nullity represent?
Consider vectors that solve Ax = 0.
What is the rank of a square matrix if all of its columns are linearly independent?
Consider the maximum independence among columns.
True or False: Nullity can be negative.
Dimensions of spaces are always non-negative.
Given matrix A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], determine the rank and nullity.
Check the relationship between row operations and linear dependence.
For a 5x4 matrix with 3 non-zero rows, what can you conclude about its nullity?
Use the Rank-Nullity theorem to find the answer.
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