Question

In the accompanying figure, sketch the vector$\overrightarrow{\mathbf{x}}$with ${\left[\overrightarrow{x}\right]}_{\mathbf{؏}}\mathbf{=}\left[\begin{array}{c}-1\\ 2\end{array}\right]$, where $\mathbf{؏}$is the basis of ${\mathbf{ℝ}}^{\mathbf{2}}$consisting of the vectors$\overrightarrow{\mathbf{v}}\mathbf{,}\overrightarrow{\mathbf{w}}$.

Short answer

If${\left[\overrightarrow{\mathrm{x}}\right]}_{؏}=\left[\begin{array}{c}-1\\ 2\end{array}\right]$where$؏$is the basis of${\mathrm{ℝ}}^2$consisting of the vectors .

Then the graph of $\overrightarrow{x}=-1\overrightarrow{v}+2\overrightarrow{w}$is

Step-by-step solution

 Sketching the vectors v→,w→

 Sketching the vectors -1v→,2w→

Since we have given that${\left[\overrightarrow{\mathrm{x}}\right]}_{؏}=\left[\begin{array}{c}-1\\ 2\end{array}\right]$, then the vector$\overrightarrow{x}=-1\overrightarrow{v}+2\overrightarrow{w}$

  Sketching the vector x→=-1v→+2w→

 Final Answer

If${\left[\overrightarrow{\mathrm{x}}\right]}_{؏}=\left[\begin{array}{c}-1\\ 2\end{array}\right]$where $؏$is the basis of${\mathrm{ℝ}}^2$consisting of the vectorslocalid="1660377766283" $\overrightarrow{v},\overrightarrow{w}$.

Then the graph oflocalid="1660377771570" $\overrightarrow{x}=-1\overrightarrow{y}+2\overrightarrow{w}$is