Dimension of a subspace and its orthogonal complement

#linear_algebra

Let $W \subset R^{5}$ be the subspace spanned by the set of vectors ${⟨ 1, - 2, 0, 2, - 1 ⟩, ⟨ - 2, 4, - 1, 1, 2 ⟩, ⟨ 0, 1, 2, - 2, 1 ⟩}$ .

Compute the dimension of $W$ .
Determine the dimension of $W^{⊥}$ , the perpendicular subspace in $R^{5}$ .
Find a basis for $W^{⊥}$ .

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L A T E X

code

Let $W\subset {\bf R}^5$ be the subspace spanned by the set of vectors $\{\langle 1,-2,0,2,-1\rangle,\langle -2,4,-1,1,2\rangle,\langle 0,1,2,-2,1\rangle\}$.
\begin{enumerate}[label=(\alph*)]
	\item Compute the dimension of $W$.
	\item Determine the dimension of $W^\perp$, the perpendicular subspace in ${\bf R}^5$.
	\item Find a basis for $W^\perp$.
\end{enumerate}