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Linear Algebra

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Orthogonal Complement: 1-Dimensional subspace

LINALG-N@57VW

Let $V$ be the subspace spanned by the vector $u=\begin{bmatrix} 1\\\ 1\\\ -1\end{bmatrix}.$

Which of the following represents the orthogonal complement, $V^{\perp}$, of $V$?

A

The line $x=y=-z$.

B

$\mathbb{R}^3$

C

The subspace of all vectors $\begin{bmatrix} x\\\ y\\\ z\end{bmatrix}$ such that:

$$2x-3y+z=0$$

D

The subspace of all vectors $\begin{bmatrix} x\\\ y\\\ z\end{bmatrix}$ such that:

$$x+y-z=0$$