포털:고등학교/수학/수학 I/문항 문서 원본 보기

<math>Q1\mathrm{.}</math> 행렬 <math>{A}\mathrm{{=}}\left({\begin{array}{ll}{3}&{2}\\{1}&{1}\end{array}}\right)</math>에 대하여 <math>{A}\mathrm{{+}}{A}^{\mathrm{{-}}{1}}</math>의 모든 성분의 합을 구하라.

<math>
{A}\mathrm{{=}}\left({\begin{array}{ll}{a}&{b}\\{c}&{d}\end{array}}\right){\mathrm{,}}\;{A}^{\mathrm{{-}}{1}}\mathrm{{=}}\frac{1}{{ad}\mathrm{{-}}{bc}}\left({\begin{array}{ll}{d}&{\mathrm{{-}}{b}}\\{\mathrm{{-}}{c}}&{a}\end{array}}\right)
</math>

<math>
{A}^{\mathrm{{-}}{1}}\mathrm{{=}}\mathrm{\left({\begin{array}{ll}{\;{1}}&{{-}{2}}\\{{-}{1}}&{\;{3}}\end{array}}\right)}
</math>

<math>
\begin{array}{ccc}{{A}\mathrm{{+}}{A}^{\mathrm{{-}}{1}}}&{\mathrm{{=}}}&{\mathrm{\left({\begin{array}{ll}{3}&{2}\\{1}&{1}\end{array}}\right)}\mathrm{{+}}\mathrm{\left({\begin{array}{ll}{1}&{{-}{2}}\\{{-}{1}}&{3}\end{array}}\right)}}\\{}&{\mathrm{{=}}}&{\mathrm{\left({\begin{array}{ll}{4}&{0}\\{0}&{4}\end{array}}\right)}}\end{array}
</math>

<math>
\begin{align}
& {{4}\mathrm{{+}}{0}\mathrm{{+}}{4}\mathrm{{+}}{0}\mathrm{{=}}{8}}\\
& {\mathrm{\therefore}\;{8}}
\end{align}
</math>