I agree with FactChecker. Just say (in words) that A is invertible. Sometimes notation is not helpful in communicating clearly.kostoglotov said:Quick question, not even sure if I should post it here, but I can't think where else. If I wanted to write the short hand of A is an invertible matrix, would it be ok to just write
[tex]A \ \exists A^{-1}[/tex]
?
A matrix is invertible if its determinant is not equal to 0. This means that the matrix has a unique solution and can be reversed to obtain the original matrix.
No, not all matrices can be inverted. Only square matrices (same number of rows and columns) with a non-zero determinant can be inverted.
The notation for an invertible matrix is A-1, where A is the original matrix and -1 represents the inverse of the matrix.
To find the inverse of a matrix, you can use the Gauss-Jordan elimination method or the adjugate matrix method. These methods involve manipulating the original matrix to obtain the inverse matrix.
An invertible matrix is important because it allows us to solve systems of equations, perform matrix operations, and find the inverse of a linear transformation. It also helps to determine the uniqueness of a solution and the rank of a matrix.