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Linear Algebra

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Vector Zero Arrow

LINALG-ZTS6GV

Can the vector:

$$\vec 0=\left [ \matrix { 0 \cr 0}\right ]$$

...be expressed as a linear combination of the vectors:

$$\vec u=\left [\matrix { 3 \cr -2}\right ], \quad \vec w=\left [\matrix { 4 \cr 4}\right ]$$

A

No, because $\vec u$ and $\vec w$ are not parallel.

B

No, because $\vec u$ and $\vec w$ are not perpendicular.

C

No, because if $a\vec u+b\vec w=\vec 0$, then $a=b=0$.

D

Yes, because $0\times \vec u+ 0\times \vec w=\vec 0$.