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2 cards from this section. Quick, good the night before a test.
What are the two properties of a linear transformation?
Think of how the transformation interacts with vector addition and scalar multiplication.
Is the function T(x) = 3x a linear transformation? Why?
Check the properties with addition and scalar multiplication.
Which of the following properties is NOT satisfied by linear transformations?
Remember the two fundamental properties!
True or False: The zero transformation is a type of linear transformation.
Does it meet the linear transformation criteria?
Prove that the transformation T: R^2 → R^2 defined by T(x, y) = (2x, 3y) is linear.
Use arbitrary u = (u1, u2) and v = (v1, v2) to simplify your proof.
Demonstrate that the transformation T given by T(x) = 5x + 2 is NOT linear.
Examine what happens with the constant addition of 2.
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