Mathematics 244 – Linear Algebra Definitions Quiz 7 – March 30, 2007

Your Name:

A) (5) Define: the coordinate vector [x]_{B} for x ∈ V with respect to the basis B for V.

B) (5) Let A = ( \begin{matrix}4 & 5 \\ 5 & 4 \end{matrix} ) and x = ( \begin{matrix}1 \\ 1 \end{matrix} ). What is the coordinate vector of Ax with respect

to the (ordered!) basis B = \{( \begin{matrix}1/2 \\ −1/2 \end{matrix} ) , ( \begin{matrix}1/2 \\ 1/2 \end{matrix} )\} for R^{2}?