Exercise 1.3.20

Question

Prove that if $\mathrm{W}$ is a subspace of a vector space $\mathrm{V}$ and $w_{1}, w_{2}, \ldots, w_{n}$ are in $\mathrm{W}$, then $a_{1} w_{1}+a_{2} w_{2}+\cdots+a_{n} w_{n} \in \mathrm{W}$ for any scalars $a_{1}, a_{2}, \ldots, a_{n}$. Visit \url{goo.gl/KTg35w} for a solution.

Jephian C.-H. Lin · Accepted Answer

\begin{proof}
We have that $a_i w_i\in W$ for all $i$. And we can get the conclusion that $a_1w_1$, $a_1w_1+a_2w_2$, $a_1w_1+a_2w_2+a_3w_3$ are in $W$ inductively.
\end{proof}

Exercise 1.3.20

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Exercise 1.3.20

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