User:IssaRice/Linear algebra/Change of basis example in two dimensions

This example comes from this video.

Jennifer's basis vectors: ${\vec{b}}_{1} : = [\begin{matrix} 2 \\ 1 \end{matrix}]$ and ${\vec{b}}_{2} : = [\begin{matrix} - 1 \\ 1 \end{matrix}]$

To Jennifer, ${\vec{b}}_{1}$ looks like $[\begin{matrix} 1 \\ 0 \end{matrix}]$ and ${\vec{b}}_{2}$ looks like $[\begin{matrix} 0 \\ 1 \end{matrix}]$ .