일차변환 행렬

$\displaystyle AB \begin{pmatrix} {1} \\ {0} \end{pmatrix} = \begin{pmatrix} {0} \\ {2} \end{pmatrix}$, $\displaystyle AB \begin{pmatrix} {0} \\ {1} \end{pmatrix} = \begin{pmatrix} {- 2} \\ {0} \end{pmatrix}$이므로 $\displaystyle AB \begin{pmatrix} {1} & {0} \\ {0} & {1} \end{pmatrix}$$\displaystyle = \begin{pmatrix} {0} & {- 2} \\ {2} & {0} \end{pmatrix}$, 즉 $AB$$\displaystyle = \begin{pmatrix} {0} & {- 2} \\ {2} & {0} \end{pmatrix}$이다. 따라서 $\displaystyle \begin{pmatrix} {2} & {1} \\ {1} & {1} \end{pmatrix} \begin{pmatrix} {a} & {b} \\ {c} & {d} \end{pmatrix}$$\displaystyle = \begin{pmatrix} {0} & {- 2} \\ {2} & {0} \end{pmatrix}$에서 $\displaystyle \begin{pmatrix} {a} & {b} \\ {c} & {d} \end{pmatrix}$$\displaystyle = {\begin{pmatrix} {2} & {1} \\ {1} & {1} \end{pmatrix}} ^{-1} \begin{pmatrix} {0} & {- 2} \\ {2} & {0} \end{pmatrix}$ $\displaystyle = \begin{pmatrix} {1} & {- 1} \\ {- 1} & {2} \end{pmatrix} \begin{pmatrix} {0} & {- 2} \\ {2} & {0} \end{pmatrix}$ $\displaystyle = \begin{pmatrix} {- 2} & {- 2} \\ {4} & {2} \end{pmatrix}$ ∴ $a = - 2$, $b = - 2$, $c = 4$, $d = 2$ ∴ $a + b + c + d$$= 2$