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2 cards from this section. Quick, good the night before a test.
Define a linear transformation.
Think about the properties that lead to maintaining the structure of vectors.
What is a coordinate transformation?
Consider how positions are represented in different frames.
What preserves operations of vector addition and scalar multiplication?
Think about how these transformations relate to operations you perform on vectors.
True or False: A stress-strain curve can be modeled using a linear transformation.
Consider if stress and strain can be represented in a mathematical framework.
A structure is designed using two different materials, one elastic and one plastic. How would the stress-strain relationship change in terms of linear transformations?
Consider the properties of each material and how they respond to forces.
Given a linear transformation matrix for a bridge analysis, how would you apply it to a coordinate system transformation?
Think about how matrix multiplication alters the dimensions of vectors.
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