Problem $1.$

Let $H_{\text{l}\text{i}\text{n}\text{e}\text{a}\text{r}}=\{h$:$R^{d}R|h(x)=w^{TT}x+b,win{R}^d,$binR$\}$ be the linear hypothesis class.

Prove that for, any $h_1,h_2,$cdots,$h_K$ in $H_{\text{l}\text{i}\text{n}\text{e}\text{a}\text{r}},$ their linear combination

$h={\displaystyle \underset{k=1}{\overset{K}{}}}{}_k{h}_k$

is also in $H_{\text{l}\text{i}\text{n}\text{e}\text{a}\text{r}},$ where ${}_k$inR.