# [SOLVED]13.2 verify that ...... is a basis for R^2 find [v]_beta

#### karush

##### Well-known member
Verify that
$\beta=\left\{\begin{bmatrix} 0\\2 \end{bmatrix} ,\begin{bmatrix} 3\\1 \end{bmatrix}\right\}$
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 $[v]_{\beta}$

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
$[v]_\beta$ denotes the coordinates of vector $v$ in basis $\beta$.

Could you say from which textbook this notation is taken?