1. 홈
  2. 계산기
  3. 계산기: 선형대수학
  4. 선형대수학 계산기

$$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]\cdot \left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right]$$$

계산기는 $$$2$$$x$$$2$$$ 행렬 $$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]$$$에 $$$2$$$x$$$2$$$ 행렬 $$$\left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right]$$$를 곱하며, 단계별 풀이를 보여 줍니다.

관련 계산기: 행렬 계산기

$$$\times$$$
A
$$$\times$$$
A

계산기가 예상대로 작동하지 않았거나 오류를 신고하거나 피드백을 공유하고 싶으시다면 문의해 주세요.

사용자 입력

$$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]\cdot \left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right]$$$을(를) 계산하세요.

풀이

$$$\left[\begin{array}{cc}{\color{Brown}5 e} & {\color{GoldenRod}\frac{2}{e^{2}}}\\{\color{Fuchsia}e} & {\color{Red}e^{-2}}\end{array}\right]\cdot \left[\begin{array}{cc}{\color{BlueViolet}\frac{1}{3}} & {\color{DarkMagenta}- \frac{2}{3}}\\{\color{Green}- \frac{1}{3}} & {\color{DeepPink}\frac{5}{3}}\end{array}\right] = \left[\begin{array}{cc}{\color{Brown}\left(5 e\right)}\cdot {\color{BlueViolet}\left(\frac{1}{3}\right)} + {\color{GoldenRod}\left(\frac{2}{e^{2}}\right)}\cdot {\color{Green}\left(- \frac{1}{3}\right)} & {\color{Brown}\left(5 e\right)}\cdot {\color{DarkMagenta}\left(- \frac{2}{3}\right)} + {\color{GoldenRod}\left(\frac{2}{e^{2}}\right)}\cdot {\color{DeepPink}\left(\frac{5}{3}\right)}\\{\color{Fuchsia}\left(e\right)}\cdot {\color{BlueViolet}\left(\frac{1}{3}\right)} + {\color{Red}\left(e^{-2}\right)}\cdot {\color{Green}\left(- \frac{1}{3}\right)} & {\color{Fuchsia}\left(e\right)}\cdot {\color{DarkMagenta}\left(- \frac{2}{3}\right)} + {\color{Red}\left(e^{-2}\right)}\cdot {\color{DeepPink}\left(\frac{5}{3}\right)}\end{array}\right] = \left[\begin{array}{cc}\frac{-2 + 5 e^{3}}{3 e^{2}} & \frac{10 - 10 e^{3}}{3 e^{2}}\\\frac{-1 + e^{3}}{3 e^{2}} & \frac{5 - 2 e^{3}}{3 e^{2}}\end{array}\right]$$$

정답

$$$\left[\begin{array}{cc}5 e & \frac{2}{e^{2}}\\e & e^{-2}\end{array}\right]\cdot \left[\begin{array}{cc}\frac{1}{3} & - \frac{2}{3}\\- \frac{1}{3} & \frac{5}{3}\end{array}\right] = \left[\begin{array}{cc}\frac{-2 + 5 e^{3}}{3 e^{2}} & \frac{10 - 10 e^{3}}{3 e^{2}}\\\frac{-1 + e^{3}}{3 e^{2}} & \frac{5 - 2 e^{3}}{3 e^{2}}\end{array}\right]\approx \left[\begin{array}{cc}4.440246191940667 & -8.609821817408108\\0.860982181740811 & -1.586629080245009\end{array}\right]$$$A