Learning Objectives
By the end of this lesson, students should be able to:
Define a linear map and identify its domain and codomain.
Determine the kernel of a linear transformation.
Determine the range of a linear transformation.
Explain why the kernel and range are vector subspaces.
Calculate the rank and nullity of a linear transformation.
Apply the Rank–Nullity Theorem to analyze the dimensions of vector spaces.
The Domain of T
The Codomain of T
The Kernel of T
The Nullity of T
The Range of T
The Rank of T
Illustration
The Rank-Nullity Theorem
Example 1
Example 2
Example 3
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