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Mathematics
         
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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.
    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\ &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} &1\ &0\ &0\ &0\ \\ &0\ &1\ &0\ &0\ \\ &0\ &0\ &1\ &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\ &4\ &2\ &8\ &5\ &7\ \\ &2\ &8\ &5\ &7\ &1\ &4\ \\ &4\ &2\ &8\ &5\ &7\ &1\ \\ &5\ &7\ &1\ &4\ &2\ &8\ \\ &7\ &1\ &4\ &2\ &8\ &5\ \\ &8\ &5\ &7\ &1\ &4\ &2\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}
    \begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &0\ &-1\ &0\ \\ &2\ &3\ &0\ \\ &1\ &-1\ &3\ \end{pmatrix}\color{black}{\ .}\\ \end{aligned}
    \begin{aligned}&\\ \color{black}{Calcu}&\color{black}{late\ the\ inverse\ matrix\ of\ } \ \ \begin{pmatrix} &-\frac{1}{2}\ &0\ &\frac{3}{2}\ \\ &-\frac{3}{2}\ &-1\ &\frac{3}{2}\ \\ &-\frac{1}{2}\ &0\ &-\frac{1}{2}\ \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.



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