What is the inverse of a matrix using determinants?
Answer (1)
The inverse of a matrix can be found using determinants if the matrix is square and its determinant is non-zero. The formula for the inverse of a matrix A is:
A^(-1) = (1 / det(A)) * adj(A)
To find the inverse, you first calculate the determinant of the matrix A. If the determinant is non-zero, you then find the adjoint (or adjugate) of the matrix. Finally, multiply the adjoint by (1 / det(A)) to obtain the inverse
If the determinant is zero, the matrix does not have an inverse. This method allows you to find the inverse of any invertible matrix using determinants and the adjoint.
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