Question

Suppose t and u are linear transformations from to such that t(ux)x for all x in. Is it true that u(tx)x for all x in ? why or why not?.

Answer 1

A linear transformation is used to illustrate a linear operator

It is true that U(T(x)) = x for all values of x

How to determine if the linear transformation is true

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:

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