Solution Found!
The following definitions are used in Exercises 28 32. Definitions. Let V be a vector
Chapter 2, Problem 28(choose chapter or problem)
The following definitions are used in Exercises 28 32. Definitions. Let V be a vector space, and let T: V V be linear. A subspace W of V is said to be T-invariant ifT(x) W for every x W, that is, T(W) C W. 7f W is T-iuvariaut, we define the restriction of T on W to be the function T w : W W defined by T w (x) = T(x) for all x W. Exercises 28-32 assume that W is a subspace of a vector space V and that T: V > V is linear. Warning: Do not assume that W is T-invariant or that T is a projection unless explicitly stated.
Questions & Answers
QUESTION:
The following definitions are used in Exercises 28 32. Definitions. Let V be a vector space, and let T: V V be linear. A subspace W of V is said to be T-invariant ifT(x) W for every x W, that is, T(W) C W. 7f W is T-iuvariaut, we define the restriction of T on W to be the function T w : W W defined by T w (x) = T(x) for all x W. Exercises 28-32 assume that W is a subspace of a vector space V and that T: V > V is linear. Warning: Do not assume that W is T-invariant or that T is a projection unless explicitly stated.
ANSWER:Step 1 of 5
To prove that 
We know that for a vector space V and a linear transformation 
Let us assume 
Then, W is a subspace of V.
Suppose
