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2331_Notes_7o1_fill - Math 2331 Linear Algebra Section 7.1...

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Math 2331 Linear Algebra Section 7.1 Linear Transformations Part 1 Let V and W be vector spaces. A function : f V W is called a linear transformation if the following conditions hold 1. For all x and y in V, f(x+y) = f(x) + f(y) 2. For all x in V and all scalars k, f(kx) = k f(x) These conditions are called "preserving the operations" because Decide whether the following maps are linear transformations - Example 1: Let be defined by : f \ \ ( ) 3 f x x = . Example 2: Let be defined by : f \ \ ( ) 1 f x x = +
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