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Linear Algebra

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Moderate

Two Elements of a Subspace of $R^3$

LINALG-XVXSFS

Suppose that:

$$\vec v=\left[\matrix {1 \cr -2 \cr 3}\right ] \hskip .1in {\rm and } \hskip .1in\vec u=\left [\matrix{ 2 \cr 3 \cr -4}\right ]$$

...are elements of a subspace $W$ of $R^3$.

Which of the following statements must be true?

Select ALL that apply.

A

$\left [ \matrix { 0\cr 0 \cr 0} \right ]\in W$

B

$\left [\matrix { 8\cr 5 \cr -6}\right ]\in W$

C

Let: $\vec x=\left [\matrix{ 0 \cr 0 \cr 1}\right ]$, then $\vec x\not \in W$.

D

$W\neq R^3$

E

The dimension of $W$ is at least $2$.

F

The dimension of $W$ is at most $2$.