Question

Suppose S,T element of L(V) are such that ST = TS. Prove that null S is invariant under T.

Answer 1

solution

for any $\upsilon$ $\in$ nul (S), S($\upsilon$) = 0

Since ST=T(T($\upsilon$))=T(S($\upsilon$)) =T(0),

Then T($\upsilon$)$\in$ nul (S) invariant under T

$$\upsilon$$