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Linear Algebra

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Moderate

Three Vectors

LINALG-NBZFLE

Suppose that $\vec v$ and $\vec w$ are non-zero elements of $R^3$.

Suppose that $\vec u$ is a linear combination of $5\vec v$ and $6\vec w$ and that $\vec u$ is not the zero vector. Which, if any, of the following are true?

Select ALL that apply.

A

If $\vec v$ and $\vec w$ are parallel, then $\vec u$ is also parallel to both $\vec v$and $\vec w$.

B

$\vec v$ can be expressed as a linear combination of $\vec w$ and $\vec u$.

C

$\vec u$ can be expressed as a linear combination of $\vec v$ and $\vec w$.

D

$6\vec w$ can be expressed as a linear combination of $\vec v$ and $\vec u$.

E

None of the above.