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Chapter 1

Chapter 1. Section 1. Examples:. 2 x 2 system. 2 x 3 system. 3 x 2 system. 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.

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Chapter 1

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  1. Chapter 1 Section 1

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

  3. The order in which any two equations are written may be interchanged System 1: System 2: (x1,x2,x3) is a solution to System 1 if any only if it is a solution to to System 2.

  4. Both sides of an equation may be multiplied by the same non zero real number. System 1: System 2: (x1,x2,x3) is a solution to System 1 if any only if it is a solution to to System 2.

  5. 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 (x1,x2,x3) 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: • The order in which any two equations are written may be interchanged. • Both sides of an equation may be multiplied by the same non-zero number • A multiple of one equation may be added to (or subtracted from) an other equation

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

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

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