1. L8 inverse of the matrix

2. 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

3. 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

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

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

6. 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

7. 1.6 Inverse of a 33 matrix Cofactor matrix of
The cofactor for each element of matrix A:

8. 1.6 Inverse of a 33 matrix
Cofactor matrix of is then given by:

9. 1.6 Inverse of a 33 matrix
Inverse matrix of is given by:

10. Properties of inverse matrices