Question

Let T: Rn → Rn be an invertible linear transformation, and let S and U be functions from Rn into Rn such that

Answer 1

Answer:

Follows are the solution to this question:

Step-by-step explanation:

$T: 1 \ R^n \to 1 \ R^n$ is invertible lines transformation

$S[T(x)]=x \ and \ V[T(x)]=x \\\\t'x \ \varepsilon\ 1 R^n$

T is invertiable linear transformation means that is  

$T(x) =A x \\\\ where \\\\ A= n \times n \ \ matrix$

and $\ det(A) \neq 0 \ \ that \ is \ \ A^{-1} \ \ exists$

Let

$V \varepsilon\ a\ R^{n} \ consider \ \ u= A^{-1} v \varepsilon 1 R^n\\\\T(u)= A(A^{-1} v)=(A \ A^{-1}) \\\\ v= I_{n \times n} \cdot v = v$

so,  

$s[T(u)]=v[T(u)]\\\\s(v)=v(v) \ \ \forall \ \ v \ \ \varepsilon \ \ 1 R^n$