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2 cards from this section. Quick, good the night before a test.
Define the kernel of a transformation.
Consider what happens to vectors during transformation.
What is the rank of a linear transformation?
Think about the dimensional space that the transformation maps to.
What does the Rank-Nullity Theorem establish?
Remember how rank and nullity relate to each other.
True or False: The dimension of the kernel is equal to the dimension of the image.
Think about how different dimensions affect transformations.
Given a transformation T from R^5 to R^2, where Ker(T) has dimension 3. Determine the rank and comment on the implications for engineering systems.
Recall how the dimensions interplay via the Rank-Nullity Theorem.
A civil engineering model uses a transformation T: R^6 -> R^3, with a null space of dimension 4. What is the rank? How does this apply to model predictions?
Apply the Rank-Nullity equation to derive ranks and summaries.
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