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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
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &-1\ &-1\ &-1\ \\ &-1\ &-1\ &-1\ \\ &-1\ &-1\ &-1\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &\frac{1}{3}\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &\frac{1}{3}\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &\frac{1}{3}\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &\frac{1}{3}\ &0\ &0\ \\ &0\ &0\ &0\ &0\ &\frac{1}{3}\ &0\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{1}{3}\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &1\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &1\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &1\ &0\ &0\ \\ &0\ &0\ &0\ &0\ &1\ &0\ \\ &0\ &0\ &0\ &0\ &0\ &1\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &2\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &4\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &6\ &0\ &0\ \\ &0\ &0\ &0\ &0\ &5\ &0\ \\ &0\ &0\ &0\ &0\ &0\ &3\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &3\ &2\ &2\ &2\ &2\ \\ &2\ &3\ &2\ &2\ &2\ \\ &2\ &2\ &3\ &2\ &2\ \\ &2\ &2\ &2\ &3\ &2\ \\ &2\ &2\ &2\ &2\ &3\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
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$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &\frac{1}{3}\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &\frac{1}{3}\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &\frac{1}{3}\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &\frac{1}{3}\ &0\ &0\ \\ &0\ &0\ &0\ &0\ &\frac{1}{3}\ &0\ \\ &0\ &0\ &0\ &0\ &0\ &\frac{1}{3}\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &1\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &1\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &1\ &0\ &0\ \\ &0\ &0\ &0\ &0\ &1\ &0\ \\ &0\ &0\ &0\ &0\ &0\ &1\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &1\ &0\ &0\ &0\ &0\ &0\ \\ &0\ &2\ &0\ &0\ &0\ &0\ \\ &0\ &0\ &4\ &0\ &0\ &0\ \\ &0\ &0\ &0\ &6\ &0\ &0\ \\ &0\ &0\ &0\ &0\ &5\ &0\ \\ &0\ &0\ &0\ &0\ &0\ &3\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &3\ &2\ &2\ &2\ &2\ \\ &2\ &3\ &2\ &2\ &2\ \\ &2\ &2\ &3\ &2\ &2\ \\ &2\ &2\ &2\ &3\ &2\ \\ &2\ &2\ &2\ &2\ &3\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}$$
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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.