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11 Nov 2019
linear algebra
Let C([-l, 1]) be the vector space of continuous functions on the interval [-1.1] and define T : C([-l, 1]) R by Thus, for example. Let f(x) = ex and g(x) = x2 for - 1 le x le 1. Show by direct computation that T(2f + 3g) = 2 T(f) + 3T(g) Is T linear? Why? Let S be the transformation defined by Show by explicit computation that . Is S linear? For the transformation S in part (c). find two functions f and g , such that . Lei U be defined by Is U linear?
linear algebra
Let C([-l, 1]) be the vector space of continuous functions on the interval [-1.1] and define T : C([-l, 1]) R by Thus, for example. Let f(x) = ex and g(x) = x2 for - 1 le x le 1. Show by direct computation that T(2f + 3g) = 2 T(f) + 3T(g) Is T linear? Why? Let S be the transformation defined by Show by explicit computation that . Is S linear? For the transformation S in part (c). find two functions f and g , such that . Lei U be defined by Is U linear?
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