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Unformatted text preview: and for those that are linear, write down the corresponding matrix. f h x y i = y 1 x g h x y i = y x h h x y i = SOLUTION Note that f is not additive: f ( u + v ) 6 = f ( u ) + f ( v ), since the second entry of f ( u + v ) is 1, while the second entry of f ( u )+ f ( v ) is 2. Thus it is not linear. (It is also not homogeneous, as you can see from almost any example you might try.) This disposes of f . The transformations g and h are both additive and homogeneous, so they are linear. By Theorem 2, the corresponding matrices are: A g = 1 1 A h = . 21 /september/ 2005; 22:09 9...
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This note was uploaded on 10/03/2010 for the course MATH 380 taught by Professor Gladue during the Fall '08 term at Roger Williams.
- Fall '08