- #1

karush

Gold Member

MHB

- 3,269

- 5

$\beta=\left\{\begin{bmatrix}

0\\2

\end{bmatrix}

,\begin{bmatrix}

3\\1

\end{bmatrix}\right\}$

is a basis for $\Bbb{R}^2$

Then for $v=\left[

\begin{array}{c}6\\8\end{array}

\right]$, find $[v]_\beta$

ok, I presume next is

$c_1\begin{bmatrix}

0\\2

\end{bmatrix}

+c_2\begin{bmatrix}

3\\1

\end{bmatrix}= \left[

\begin{array}{c}6\\8\end{array}

\right]$

by augmented matrix we get (the book did this?)

$\left[ \begin{array}{cc|c} 0 & 3 & 6 \\ 2 & 1 & 8 \end{array} \right]

=\left[ \begin{array}{cc|c} 1 & 0 & 3 \\ 0 & 1 & 2 \end{array} \right]$

hence

$[v]_{\beta}=\left[

\begin{array}{c}3\\2\end{array}

\right]$

following an example I don't think I understand the notation of $[v]_{\beta}$