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4 cards from this section. Quick, good the night before a test.
Define the kernel of a linear transformation.
Think about what happens when you apply T to some vectors.
What is the range of a linear transformation?
Consider all possible images that can be created from a set of inputs.
What is the kernel of a linear transformation?
Think about what inputs give zero outputs in the transformation.
True or False: The range of a linear transformation can be larger than the codomain.
Consider the relationship between outputs and the broader space.
Given the matrix A = [[1, 2], [3, 4]], analyze the kernel and range. Determine if the transformation is injective.
Consider both null space and image through operations on matrix A.
If the transformation T represented by a 4x3 matrix has a kernel dimension of 1, what is the maximum rank of this transformation?
Apply the theorem to deduce the rank from given dimensions.
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