演習問題

次のような2つの線形写像 ${\displaystyle f}$ と${\displaystyle g}$がある．

• ${\displaystyle f ：R^3\to R^2}$

  ${\displaystyle \left(\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right)\to \left(\begin{array}{c}{x}_1+2x_2\\ x_2-x_3\end{array}\right)}$

• ${\displaystyle g：R^2\to R^2}$

  $\left(\begin{array}{c}{x_1}^{\prime }\\ {x_2}^{\prime }\end{array}\right)\to \left(\begin{array}{c}{x_1}^{\prime }-{x_2}^{\prime }\\ -2{x_2}^{\prime }\end{array}\right)$

${\displaystyle f}$ と${\displaystyle g}$ の表現行列 ${\displaystyle A}$と ${\displaystyle B}$を求めよ．