Thread: Linear Algebra please help.

Let V, W, and Z be vector spaces, and let T: V-->V. Prove that T[T(v)]= 0 if and only if R(T) is a subset of N(T).

Originally Posted by JCIR

Let V, W, and Z be vector spaces, and let T: V-->V. Prove that T[T(v)]= 0 if and only if R(T) is a subset of N(T).

Step 1:

CLAIM:

Proof:

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Step 2:
CLAIM:

Proof: