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\leftline{Mathematics 244 -- Linear Algebra}
\leftline{Definitions Quiz 7 -- March 30, 2007}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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A) (5) Define: the coordinate vector $[x]_B$ for $x \in V$ with respect
to the basis $B$ for $V$.  
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B) (5)  Let $A = \pmatrix{4 & 5\cr 5 & 4\cr}$ and $x = \pmatrix{1 \cr 1\cr}$.
What is the coordinate vector of $Ax$ with respect to the (ordered!) basis
$B = \left\{\pmatrix{1/2\cr -1/2\cr}, \pmatrix{1/2\cr 1/2\cr}\right\}$
for ${\bf R}^2$?  
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