Invert Command

Invert( <Matrix> )

Inverts the given matrix.

Example: Invert({{1, 2}, {3, 4}}) yields \begin{pmatrix}-2 & 1\\1.5 & -0.5\end{pmatrix}, the inverse matrix of \begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}.

Note: In the CAS View undefined variables are allowed too.

Example:

Invert({{a, b}, {c, d}}) yields \begin{pmatrix}\frac{d}{ad- bc} & \frac{-b}{ad- bc}\\\frac{-c}{ad- bc}& \frac{a}{ ad- bc}\end{pmatrix}, the inverse matrix of \begin{pmatrix}a & b\\c & d\end{pmatrix}.

Invert( <Function> )

Gives the inverse of the function.

Example:

Invert(sin(x)) yields asin(x).

Note:

The function must contain just one x and no account is taken of domain or range, for example for f(x) = x^2 or f(x) = sin(x).
If there is more than one x in the function another command might help you:

Example:

Both Invert(PartialFractions((x + 1) / (x + 2))) and Invert(CompleteSquare(x^2 + 2 x + 1)) yield the inverse functions.

Note:

• In the CAS View, the command also works if the function contains more than one x.
• See also Eigenvalues Command, Eigenvectors Command, SVD Command, Transpose Command, JordanDiagonalization Command