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6 Nov 2019
solve this quastions and show all works :
Decide (without proof) which of the following maps are linear. f : R2 rightarrow R3 with f(x, y) = (2x - y, xy, x). f : R2 rightarrow R3 with f(x, y) = (x - y, 0, x + y). f : R2 rightarrow R2 with f(x, y) = (x + 1, y + 1). Decide (without proof) which of the following maps are linear, where V is a suitable subspace of all the functions from R to R. T : V rightarrow V with (T(f)) (x) = f''(x) + 2xf'(x) + x2f(x). T : V rightarrow R with T(f) = f(x) sin(x) dx. T : V rightarrow V with (T(f)) (x) = f'(2x). Show transcribed image text
solve this quastions and show all works :
Decide (without proof) which of the following maps are linear. f : R2 rightarrow R3 with f(x, y) = (2x - y, xy, x). f : R2 rightarrow R3 with f(x, y) = (x - y, 0, x + y). f : R2 rightarrow R2 with f(x, y) = (x + 1, y + 1). Decide (without proof) which of the following maps are linear, where V is a suitable subspace of all the functions from R to R. T : V rightarrow V with (T(f)) (x) = f''(x) + 2xf'(x) + x2f(x). T : V rightarrow R with T(f) = f(x) sin(x) dx. T : V rightarrow V with (T(f)) (x) = f'(2x).
Show transcribed image text Beverley SmithLv2
21 May 2019