Chapter 5.4, Problem 43E

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.

$\left(\text{a}\right)$ The orthogonal complement of $R^n$ is empty set.

$\left(\text{b}\right)$ If each vector $v\in R^n$ can be uniquely written as a sum of a vector $s_1$ from $S_1$ and a vector $s_2$ from $S_2$, then $R^n$ is direct sum of $S_1$ and $S_2$.