Find the domain and codomain of T3 T2 T1, and find (T3 T2 T1)(x, y). T1(x, y) =

Question

Find the domain and codomain of T3 T2 T1, and find (T3 T2 T1)(x, y). T1(x, y) = (- 5y, 8x, x - 5y), T2(x, y, z) = (y, z, x), T3(x, y, z) = (x + z, y - z) The domain and codomain of T3 T2 T1 are R3, and (T3 T2 T1)(x, y) = (8x - 5y, x, - 5y). The domain and codomain of T3 T2 T3 are R2, and (T3 T2 T3)(x, y) = (8x - 5y, x). The domain and codomain of T3 T2 T1 are R3, and (T3 T2 T1)(x, y) = (x, 8x - 5y). The domain and codomain of T3 T2 T1 are R3, and (T3 T2 T1)(x, y) = (8x - 5y, x). The domain and codomain of T3 T2 T3 are R2, and (T3 T2 T3)(x, y) = (x, 8x - 5y).

Explanation / Answer

T3 o T2 o T1(x,y)=T3 o T2(-5y,8x,x-5y)= T3(8x,x-5y,-5y) =(8x-5y,x) The domain of T1 (which is the same as domain of T3 o T2 o T1) is R^2 Answer b)

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