Section 2.4 When the Scalar Multiple is 1
Checkpoint 2.4.1.
What is the notation for the additive inverse of \(-\mathbf{Q}\text{?}\) Find a vector other than \(\mathbf{Q}\) which satisfies the definition of additive inverse for \(-\mathbf{Q}\text{.}\)
Checkpoint 2.4.2.
Show: \(-(-\mathbf{Q})=1\mathbf{Q}\text{.}\)
Checkpoint 2.4.3.
Can a linear space have exactly one element? Include justification.
Theorem 2.4.4.
For any point \(\mathbf{P}\) in linear space \(\mathbb{L}\text{:}\)
\begin{equation*}
1\mathbf{P} = \mathbf{P}
\end{equation*}
Challenge 2.4.5.
Can a linear space have exactly two elements?