LINEAR ALGEBRA (Math 211)
Sheet #2

Multiplication of matrices.

Matrix representation of a linear system:

Indentity matrix: .
 Inverse matrix:

Solving a sytem of n linear equations of n variables:

An elementary matrix is a matrix which can be obtained from an identity matrix by one of the following tree operations:

Theorem. If E is an elementary matrix then the matrix is obtained from matrix A by the row operation (1)-(3) corrsponding to E.

 Examples.

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: .

LINEAR ALGEBRA (Math 211)
HW #3 (Due Mon. Sept. 25 )

Multiply the following matrices.

1. 2.

Find the following inverses.

 3 4
5. , if .

LINEAR ALGEBRA (Math 211)
HW #4 (Due Wed. Sept. 27)

Find the following inverses and their representation as the product of elementary matrices.

1. 2.

Find the inverses.

3. 4.

5. Solve matrix equation