1. Chapter 1 Section 1

2. Examples: 2 x 2 system 2 x 3 system 3 x 2 system

3. 1.The order in which any two equations are written may be interchanged System 1:System 2: (x 1,x 2,x 3 ) is a solution to System 1 if any only if it is a solution to to System 2.

4. 2.Both sides of an equation may be multiplied by the same non zero real number. System 1:System 2: (x 1,x 2,x 3 ) is a solution to System 1 if any only if it is a solution to to System 2.

5. 3.A multiple of one equation may be added to (or subtracted from) another. System 1:System 2: *Multiply Equation 2 by 2 and add it to Equation 1 (x 1,x 2,x 3 ) is a solution to System 1 if any only if it is a solution to to System 2.

6. The following three operations may be used on a system to obtain an equivalent system: 1.The order in which any two equations are written may be interchanged. 2.Both sides of an equation may be multiplied by the same non-zero number 3.A multiple of one equation may be added to (or subtracted from) an other equation

7. Elementary Row Operations: 1.Interchange two rows 2.Multiply a row by a non-zero real number 3.Replace a row by its sum with a multiple of an other row

8. Steps for reducing linear systems: Step 1 Step 2 Step 3