行列計算機
行列を段階的に解く
この計算機は、途中の手順を示しながら、2つの行列の加算・減算・乗算・除算およびべき乗を行います。さらに、行列式、逆行列、rref（既約行階段形）、零空間、階数、固有値、固有ベクトルを求め、行列にスカラーを掛けることもできます。
入力内容
$$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 0 & 4\\0 & 1 & 0\end{array}\right] + \left[\begin{array}{ccc}2 & 1 & 4\\5 & 7 & 1\\1 & 2 & 5\end{array}\right]$$$を計算せよ。
解答
$$$\left[\begin{array}{ccc}{\color{OrangeRed}1} & {\color{DarkBlue}0} & {\color{DeepPink}0}\\{\color{Crimson}0} & {\color{Peru}0} & {\color{Magenta}4}\\{\color{Fuchsia}0} & {\color{GoldenRod}1} & {\color{DarkMagenta}0}\end{array}\right] + \left[\begin{array}{ccc}{\color{OrangeRed}2} & {\color{DarkBlue}1} & {\color{DeepPink}4}\\{\color{Crimson}5} & {\color{Peru}7} & {\color{Magenta}1}\\{\color{Fuchsia}1} & {\color{GoldenRod}2} & {\color{DarkMagenta}5}\end{array}\right] = \left[\begin{array}{ccc}{\color{OrangeRed}\left(1\right)} + {\color{OrangeRed}\left(2\right)} & {\color{DarkBlue}\left(0\right)} + {\color{DarkBlue}\left(1\right)} & {\color{DeepPink}\left(0\right)} + {\color{DeepPink}\left(4\right)}\\{\color{Crimson}\left(0\right)} + {\color{Crimson}\left(5\right)} & {\color{Peru}\left(0\right)} + {\color{Peru}\left(7\right)} & {\color{Magenta}\left(4\right)} + {\color{Magenta}\left(1\right)}\\{\color{Fuchsia}\left(0\right)} + {\color{Fuchsia}\left(1\right)} & {\color{GoldenRod}\left(1\right)} + {\color{GoldenRod}\left(2\right)} & {\color{DarkMagenta}\left(0\right)} + {\color{DarkMagenta}\left(5\right)}\end{array}\right] = \left[\begin{array}{ccc}3 & 1 & 4\\5 & 7 & 5\\1 & 3 & 5\end{array}\right]$$$
解答
$$$\left[\begin{array}{ccc}1 & 0 & 0\\0 & 0 & 4\\0 & 1 & 0\end{array}\right] + \left[\begin{array}{ccc}2 & 1 & 4\\5 & 7 & 1\\1 & 2 & 5\end{array}\right] = \left[\begin{array}{ccc}3 & 1 & 4\\5 & 7 & 5\\1 & 3 & 5\end{array}\right]$$$A