16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.5.11

Linear Transformations

Mathematics — Linear Algebra · annihilator-sum-and-intersection

Problem

Let

W_1

and

W_2

be subspaces of a finite-dimensional vector space

V

. (a) Prove that

(W_1 + W_2)^0 = W_1^0 \cap W_2^0

. (b) Prove that

(W_1 \cap W_2)^0 = W_1^0 + W_2^0