Let $v_1,v_2,v_3,p,q \in \mathbb{R}_2[x]$. We have that $p=a+bx+cx^2, q = a'+b'x+c'x^2$. The scalar product in $\mathbb{R}_2[x]$ is defined as $\left \langle p,q \right \rangle=aa'+2bb'+cc'$
$v_1= \begin{pmatrix} 2\\ 0\\ 0 \end{pmatrix}, v_2=\begin{pmatrix} 0\\ 1\\ 1 \end{pmatrix}, v_3=\begin{pmatrix} 1\\ 0\\ 1 \end{pmatrix}$
Calculate $\left \| v_1 \right \|, \left \langle v_1,v_2 \right \rangle, \left \| v_1+v_2 \right \|$
Could you please tell me if I do it correct?
$\left \| v_1 \right \|= \sqrt{2^2+0^2+0^2}= \sqrt{4}=2$
$\left \langle v_1,v_2 \right \rangle= 2 \cdot 0+2 \cdot 0 \cdot 1 +0 \cdot 1 =0$
$\left \| v_1+v_2 \right \|= \sqrt{2^2+0^2+0^2+0^2+1^2+1^2}= \sqrt{6}$