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2 cards from this section. Quick, good the night before a test.
Define a linear transformation.
Think about operations that must be preserved.
What is a standard matrix?
How does it relate to the transformation of basis vectors?
What does the standard matrix of a linear transformation represent?
Consider how matrices simplify transformations.
True or False: Every linear transformation can be represented by a matrix.
Reflect on the definition of linear transformations.
Given a linear transformation T: R² → R² that reflects points across the x-axis. Derive the standard matrix for this transformation.
Consider how the reflection across the x-axis affects points.
Suppose T is a rotation transformation through an angle α. Create a general expression for its standard matrix.
Think about how angles are represented in rotation.
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