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Get the inverse matrix:
Enter an invertible matrix, with each element separated by a comma and each row ending with a semicolon.
Note that mathematical functions and variables are not supported.
Enter an invertible matrix, with each element separated by a comma and each row ending with a semicolon.
Note that mathematical functions and variables are not supported.
Current location：Linear algebra >Inverse matrix >History of inverse matrices
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &4\ &3\ &3\ &3\ &3\ &3\ \\ &3\ &4\ &3\ &3\ &3\ &3\ \\ &3\ &3\ &4\ &3\ &3\ &3\ \\ &3\ &3\ &3\ &4\ &3\ &3\ \\ &3\ &3\ &3\ &3\ &4\ &3\ \\ &3\ &3\ &3\ &3\ &3\ &4\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &2\ &2\ &1\ &1\ &1\ &1\ \\ &1\ &2\ &2\ &1\ &1\ &1\ \\ &1\ &1\ &2\ &2\ &1\ &1\ \\ &1\ &1\ &1\ &2\ &2\ &1\ \\ &1\ &1\ &1\ &1\ &2\ &2\ \\ &2\ &1\ &1\ &1\ &1\ &2\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &12\ &1\ &2\ &34\ &3\ &4\ \\ &56\ &5\ &6\ &78\ &7\ &8\ \\ &13\ &1\ &3\ &57\ &5\ &7\ \\ &24\ &2\ &4\ &68\ &6\ &8\ \\ &15\ &1\ &5\ &26\ &2\ &6\ \\ &37\ &3\ &7\ &48\ &4\ &8\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &12\ &34\ &1\ &2\ &3\ &4\ \\ &56\ &78\ &5\ &6\ &7\ &8\ \\ &13\ &57\ &1\ &3\ &5\ &7\ \\ &24\ &68\ &2\ &4\ &6\ &8\ \\ &15\ &26\ &1\ &5\ &2\ &6\ \\ &37\ &48\ &3\ &7\ &4\ &8\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &1\ &1\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ &1\ &2\ \\ &1\ &1\ &1\ &1\ &2\ &3\ \\ &1\ &1\ &1\ &2\ &3\ &4\ \\ &1\ &1\ &2\ &3\ &4\ &5\ \\ &1\ &2\ &3\ &4\ &5\ &6\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
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$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &2\ &2\ &1\ &1\ &1\ &1\ \\ &1\ &2\ &2\ &1\ &1\ &1\ \\ &1\ &1\ &2\ &2\ &1\ &1\ \\ &1\ &1\ &1\ &2\ &2\ &1\ \\ &1\ &1\ &1\ &1\ &2\ &2\ \\ &2\ &1\ &1\ &1\ &1\ &2\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &12\ &1\ &2\ &34\ &3\ &4\ \\ &56\ &5\ &6\ &78\ &7\ &8\ \\ &13\ &1\ &3\ &57\ &5\ &7\ \\ &24\ &2\ &4\ &68\ &6\ &8\ \\ &15\ &1\ &5\ &26\ &2\ &6\ \\ &37\ &3\ &7\ &48\ &4\ &8\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &12\ &34\ &1\ &2\ &3\ &4\ \\ &56\ &78\ &5\ &6\ &7\ &8\ \\ &13\ &57\ &1\ &3\ &5\ &7\ \\ &24\ &68\ &2\ &4\ &6\ &8\ \\ &15\ &26\ &1\ &5\ &2\ &6\ \\ &37\ &48\ &3\ &7\ &4\ &8\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &1\ &1\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ &1\ &2\ \\ &1\ &1\ &1\ &1\ &2\ &3\ \\ &1\ &1\ &1\ &2\ &3\ &4\ \\ &1\ &1\ &2\ &3\ &4\ &5\ \\ &1\ &2\ &3\ &4\ &5\ &6\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
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Elementary transformations of matrices:
Definition:Applying the following three transformations to the rows (columns) of a matrix becomes the elementary transformation of the matrix：
(1) Swap the positions of two rows (columns) in a matrix;
(2) Using non-zero constants λ Multiply a certain row (column) of a matrix;
(3) Convert a row (column) of a matrix γ Multiply to another row (column) of the matrix.