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17 Jun 2022
Let T: V ? W and S: W ? V be linear transformations. (a) If ST = I (I: V ? V is the identity transformation, I(v) = v for every v ? V), show that W = range(T) ? ker(S). (Hint: Show that if w ? W, w ? TS(w) ? ker(S)) (b) Illustrate part (a) with T: R^2 ? R^3, and S: R^3 ? R^2 given by T(x,y) = (x,y,0), and S(x,y,z) =(x, y).
Let T: V ? W and S: W ? V be linear transformations. (a) If ST = I (I: V ? V is the identity transformation, I(v) = v for every v ? V), show that W = range(T) ? ker(S). (Hint: Show that if w ? W, w ? TS(w) ? ker(S)) (b) Illustrate part (a) with T: R^2 ? R^3, and S: R^3 ? R^2 given by T(x,y) = (x,y,0), and S(x,y,z) =(x, y).
paupauLv4
19 Jun 2022
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