Determine whether {v 1 , v 2 , v 3 } is a basis for R 3
-$$B = \left\{ \left[ \begin{array} { r }
- 2 \
2
\end{array} \right] , \left[ \begin{array} { l }
0 \
1
\end{array} \right] \right\} , [ \mathrm { x } ] _ { B } = \left[ \begin{array} { r }
- 5 \
5
\end{array} \right]$$
A)

$\left[ \begin{array} { r } - 2 \ 3 \end{array} \right]$

B)
$\left[ \begin{array} { c } 10 \ - 5 \end{array} \right]$

C)
$\left[ \begin{array} { r } 10 \ 5 \end{array} \right]$

D)

$\left[ \begin{array} { r } - 10 \ - 5 \end{array} \right]$

Question

Determine whether {v 1 , v 2 , v 3 } is a basis for R 3 
-$$B = \left\{ \left[ \begin{array} { r } 
- 2 \
2
\end{array} \right] , \left[ \begin{array} { l } 
0 \
1
\end{array} \right] \right\} , [ \mathrm { x } ] _ { B } = \left[ \begin{array} { r } 
- 5 \
5
\end{array} \right]$$
A)

$\left[ \begin{array} { r } - 2 \ 3 \end{array} \right]$

B)
$\left[ \begin{array} { c } 10 \ - 5 \end{array} \right]$

C)
$\left[ \begin{array} { r } 10 \ 5 \end{array} \right]$

D)

$\left[ \begin{array} { r } - 10 \ - 5 \end{array} \right]$

Quizplus · Accepted Answer

Given $[x]_B = \left[ \begin{array} { r } -5 \ 5 \end{array} \right]$ and $B = \left\{ \left[ \begin{array} { r } -2 \ 2 \end{array} \right], \left[ \begin{array} { l } 0 \ 1 \end{array} \right] \right\}$, to find $x$ in the standard basis, we compute $x = -5\left[ \begin{array} { r } -2 \ 2 \end{array} \right] + 5\left[ \begin{array} { l } 0 \ 1 \end{array} \right] = \left[ \begin{array} { c } 10 \ -5 \end{array} \right]$.

Determine Whether {V1, V2, V3} Is a Basis for R3

Determine Whether {V₁, V₂, V₃} Is a Basis for R³