L8 inverse of the matrix

The Inverse of a Matrix (A-1) For an n  n matrix A, there may be a B such that AB = I = BA. The inverse is analogous to a reciprocal A matrix which has an inverse is nonsingular. A matrix which does not have an inverse is singular. An inverse exists only if

Singular Matrix Singular Matrix: A matrix is considered singular if the determinant of the matrix is zero The matrix cannot be inverted Usually caused by linear dependencies between vectors When a matrix is not full rank An extreme form of multicollinearity in the matrix

How to find inverse matrixes? determinants? and more? If and |A|  0 Otherwise, use SAS/IML an easier way

Matrix Inverse Matrix Inverse: For a 2x2 matrix the inverse is relatively simple For anything else, use a computer…

1.5 Determinants of order 3 Consider an example: Its determinant can be obtained by: You are encouraged to find the determinant by using other rows or columns

1.6 Inverse of a 33 matrix Cofactor matrix of The cofactor for each element of matrix A:

1.6 Inverse of a 33 matrix Cofactor matrix of is then given by:

1.6 Inverse of a 33 matrix Inverse matrix of is given by:

Properties of inverse matrices