演習問題

${\displaystyle A=\left(\begin{array}{cc}-2& 1\\ 1& 2\end{array}\right)}$ ， ${\displaystyle B=\left(\begin{array}{cc}1& 2\\ -6& 9\end{array}\right)}$ のとき，次の行列を求めよ．

[i]等式${\displaystyle A-2X=\frac{1}{3}\left\{4A-3\left(B+3X\right)\right\}}$ を満たす行列${\displaystyle X}$

[ii]2つの等式${\displaystyle P+Q=A}$ ，${\displaystyle P-Q=B}$ を同時に満たす2次の正方行列${\displaystyle P}$ ，${\displaystyle Q}$

${\displaystyle A=\left(\begin{array}{cc}5& 3\\ -7& -10\end{array}\right)}$ ， ${\displaystyle B=\left(\begin{array}{cc}-2& 5\\ 1& -9\end{array}\right)}$ のとき，次の行列を求めよ．

[i]等式${\displaystyle \frac{2}{5}A-\frac{2}{3}X=\frac{1}{6}\left\{-2A-\left(2X-3B\right)\right\}}$ を満たす行列${\displaystyle X}$

[ii]2つの等式${\displaystyle PQ=A}$…(1) ，${\displaystyle P=A+B}$…(2) を同時に満たす2次の正方行列${\displaystyle P}$，${\displaystyle Q}$を求めよ．

${\displaystyle A=\left(\begin{array}{cc}-3& 5\\ 2& 1\end{array}\right)}$ ， ${\displaystyle B=\left(\begin{array}{cc}2& -3\\ -1& 7\end{array}\right)}$ のとき，次の行列を求めよ．

[i]等式${\displaystyle A^2+\frac{1}{2}X=\frac{1}{6}\left\{2B^2-3\left(X-2A^2\right)\right\}}$ を満たす行列${\displaystyle X}$

[ii]2つの等式${\displaystyle 2\left(P+Q\right)=A}$，${\displaystyle \frac{1}{3}\left(P-Q\right)=B}$を同時に満たす2次の正方行列${\displaystyle P}$ ，${\displaystyle Q}$