Unformatted text preview: and for those that are linear, write down the corresponding matrix. f Âµh x y iÂ¶ = Â± y 1 x Â² g Âµh x y iÂ¶ = Â± y x Â² h Âµh x y iÂ¶ = Â± Â² 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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 Fall '08
 Gladue
 Calculus, Vector Space, Following

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