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2 cards from this section. Quick, good the night before a test.
What is a linear transformation?
Think about how vectors behave under addition.
Define the kernel of a linear transformation.
Focus on what happens to vectors in the mapping.
What does a linear transformation preserve?
Look back at the properties defined.
True or False: The kernel of a linear transformation is the set of all vectors mapped to zero.
Remember the definition of kernel.
Given the linear transformation T: R^3 → R^3 represented by the matrix [[1, 2, 3], [0, 1, 4], [0, 0, 0]], determine the kernel of this transformation.
Set up the equation involving your transformation matrix and find when it results in the zero vector.
If a linear transformation has a rank of 2 and operates on a 4-dimensional space, what is the dimension of the kernel?
Remember the rank-nullity theorem connects dimensions; you have the rank and domain.
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