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konstantin123 [22]
2 years ago
6

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

Mathematics
1 answer:
ipn [44]2 years ago
7 0

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

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