Multiplication of matrices.
Matrix representation of a linear system:
Indentity matrix: .
Inverse matrix:

Solving a sytem
of n linear equations of n
variables:
Theorem. If E is an elementary matrix then the matrix is obtained from matrix A by the row operation (1)(3) corrsponding to E.


Multiplication of the first row by 5  Interchanging of the first and third rows  Addition 7 times the first row to the third row 
A method for inverting matrices.
Adjoin the identity matrix I to the right side of A producing .
Apply row operations (1)(3) to this matrix until the left half is reduced to I. The right half will be converted into the inverse matrix: .
Multiply the following matrices.
1. 2.
Find the following inverses.
3.

4. 
Find the following inverses and their representation as the
product of elementary matrices.
1. 2.
Find the inverses.
3. 4.
5. Solve matrix equation