Solution: True or False In Exercises 43 and 44, determine

Chapter 5, Problem 43

(choose chapter or problem)

True or False? In Exercises 43 and 44, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

(a) The orthogonal complement of \(R^{n}\) is the empty set.

(b) If each vector \(\mathbf{v} \in R^{n}\) can be uniquely written as a sum of a vector \(\mathbf{s}_{1}\) from \(S_{1}\) and a vector \(\mathbf{s}_{2}\) from \(S_{2}\), then \(R^{n}\) is the direct sum of \(S_{1}\) and \(S_{2}\).

Text Transcription:

R^n

v in R^n

s_1

S_1

s_2

S_2