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Linear Algebra

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Coordinate Vector for $\vec u$

LINALG-JINWQG

$${\cal B}=\left \{ \left [\matrix { 1 \cr 0 \cr 1}\right ], \left [\matrix { 0\cr 1 \cr 1}\right], \left [\matrix { 1 \cr 1 \cr 0}\right ]\right \}$$

...is a basis for $R^3$.

$$\vec u=\left[\matrix {1 \cr 1 \cr 1}\right ]$$

...is a vector in $R^3$.

Which, if any, of the following is $[\vec u]_{\cal B}$, the coordinate vector of $\vec u$ with respect to ${\cal B}$?

A

$[\vec u]_{\cal B}= \left [\matrix { 1 \cr 1 \cr 1}\right ]$

B

$[\vec u]_{\cal B} =\left [\matrix { 1/2 \cr 1/2 \cr 1/2}\right ]$

C

None of the above.