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2 cards from this section. Quick, good the night before a test.
Define the kernel of a linear transformation.
Think about what happens when inputs lead to zero outputs.
What is the range of a linear transformation?
Consider the images of all input vectors.
What is the kernel of a linear transformation?
Think about inputs that cause no change.
The range of T is the set of all vectors mapped to [0] in the codomain. True or False?
Focus on the outputs of the transformation.
Given a linear transformation T: R^3 → R^3 defined by T(x, y, z) = (x + y - z, 2y, -x + z), find the kernel and range.
Use matrix representation if necessary to analyze.
How does a change in dimension of the kernel affect the system of equations represented in a transformation?
Relate to the implications of the Rank-Nullity theorem.
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