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Calculus: perpendicular planes in $\mathbb{R}^4$

Let $W \leq \mathbb{R}^n$ and set $$W^{\perp} = \{v \in \mathbb{R}^n | v.w =0, \hspace{0.25cm} \forall w \in W\}$$ (a) Show that $W^{\perp} \leq \mathbb{R}^n$.

(b) Let $v_1=\langle 1, 1, 1, 2\rangle$,$v_2=\langle 2, 1, 1, 1\rangle$, and $v_3=\langle -1, 2, 2, 7\rangle$. Let $T: \mathbb{R}^3 \rightarrow \mathbb{R}^4$ be the transformation given by $e_1 \mapsto v_1$, $e_2 \mapsto v_2$, and $e_3 \mapsto v_3$.Let $W=img(T)$. Find a basis for $W$ and $W^{\perp}$.

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