A linear transformation is used to illustrate a linear operator
It is true that U(T(x)) = x for all values of x
The linear functions are given as:
U(x1) and U(x2)
Given that the function U(x) is a one-one-one function, then we have:
T(U(x1)) = T(U(x2))
This becomes
x1 = x2
The above equations mean that the function U is invertible
So, we have:
S(U(x)) = U(S(x)) = x for all values of x
Also, we have:
T(U(x)) = x for all values of x.
This means that,
T(x) = S(x) and U(T(x)) = x for all values of x, because U(S(x)) = x for all values of x
Hence, it is true that U(T(x)) = x for all values of x
Read more about linear transformations at:
https://brainly.com/question/1599831
