$$$\left[\begin{array}{cc}2 & 1\\3 & 4\end{array}\right]$$$의 의사역함수

$$$\left[\begin{array}{cc}2 & 1\\3 & 4\end{array}\right]$$$의 무어-펜로즈 의사역행렬을 구하시오.

행렬 $$$A$$$의 유사역행렬은 $$$A^{+} = A^{T} \left(A A^{T}\right)^{-1}$$$입니다.

다음 행렬의 전치행렬을 구하십시오: $$$\left[\begin{array}{cc}2 & 1\\3 & 4\end{array}\right]^{T} = \left[\begin{array}{cc}2 & 3\\1 & 4\end{array}\right]$$$ (단계별 과정은 행렬 전치 계산기를 참조하세요.)

원래 행렬에 그 전치행렬을 곱하십시오:

$$$\left[\begin{array}{cc}2 & 1\\3 & 4\end{array}\right]\cdot \left[\begin{array}{cc}2 & 3\\1 & 4\end{array}\right] = \left[\begin{array}{cc}5 & 10\\10 & 25\end{array}\right]$$$ (단계는 행렬 곱셈 계산기를 참조하세요).

역행렬을 구하세요: $$$\left[\begin{array}{cc}5 & 10\\10 & 25\end{array}\right]^{-1} = \left[\begin{array}{cc}1 & - \frac{2}{5}\\- \frac{2}{5} & \frac{1}{5}\end{array}\right]$$$ (단계별 풀이가 필요하면 역행렬 계산기를 참조하세요).

마지막으로, 행렬을 곱하십시오:

$$$\left[\begin{array}{cc}2 & 3\\1 & 4\end{array}\right]\cdot \left[\begin{array}{cc}1 & - \frac{2}{5}\\- \frac{2}{5} & \frac{1}{5}\end{array}\right] = \left[\begin{array}{cc}\frac{4}{5} & - \frac{1}{5}\\- \frac{3}{5} & \frac{2}{5}\end{array}\right]$$$ (단계는 행렬 곱셈 계산기를 참조하세요).

$$$\left[\begin{array}{cc}2 & 1\\3 & 4\end{array}\right]^{+} = \left[\begin{array}{cc}\frac{4}{5} & - \frac{1}{5}\\- \frac{3}{5} & \frac{2}{5}\end{array}\right] = \left[\begin{array}{cc}0.8 & -0.2\\-0.6 & 0.4\end{array}\right]$$$A