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Linear Algebra

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Moderate

Vector Distance: Matrix Products and Linear Combinations

LINALG-GCSB36

If $\boldsymbol{u} = \begin{bmatrix} 1\\\ 0\\\ -1\end{bmatrix}$, $\boldsymbol{v} = \begin{bmatrix} 0\\\ -5\\\ 3\end{bmatrix}$, $\boldsymbol{w} = \begin{bmatrix} -1\\\ 0\\\ -3\end{bmatrix}$, $A = \begin{bmatrix} 2&-2&-3\\\ 1&0&-1\\\ 3&-1&1\end{bmatrix}$, and $B = \begin{bmatrix} 1&-1&1\\\ 0&2&0\\\ 3&3&-1\end{bmatrix}$

...then compute the distance between $A\boldsymbol{u}$ and $B(\boldsymbol{v}-2\boldsymbol{w})$

A

$\sqrt{107}$

B

$3\sqrt{14}$

C

$\sqrt{665}$

D

$\sqrt{42}$

E

$2\sqrt{2}$

F

$\sqrt{146}$