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The following definitions are used in Exercises 23 30. Definition. If S\ and S2 are
Chapter 1, Problem 23(choose chapter or problem)
The following definitions are used in Exercises 23 30. Definition. If S\ and S2 are nonempty subsets of a vector space V. then the sum of Si and S2, denoted S\ +S2, is the set [x+y: x S\ and y S2}. Definition. A vector space V is called the direct sum of W] and VV2 if W, and W2 are subspaces of'W such that W2 D W2 = {0} and W, +W2 = V. Wc denote that V is the direct sum of W] and W2 by writing V = W, W2.
Questions & Answers
QUESTION:
The following definitions are used in Exercises 23 30. Definition. If S\ and S2 are nonempty subsets of a vector space V. then the sum of Si and S2, denoted S\ +S2, is the set [x+y: x S\ and y S2}. Definition. A vector space V is called the direct sum of W] and VV2 if W, and W2 are subspaces of'W such that W2 D W2 = {0} and W, +W2 = V. Wc denote that V is the direct sum of W] and W2 by writing V = W, W2.
ANSWER:Step 1 of 3
(a)
It is given that 
By definition if 
