HW Examples

 

  1. Solve the following set of linear equations using
    1. Gauss elimination
    2. Gauss Jordan reduction
    3. Inverse of the coefficient matrix

 

x1   + 2x2 – x3 – 2x4 = -1

2x1 +  x2  + x3  –  x4 = 4

x1  +  x2  +2x3  +  x4 = 5

x1  + 3x2 +2x3 - 3x4 = -3

 

  1.   For the following set of linear equations
    1. Check if the system has a unique solution
    2. Solve the system using Gauss elimination
    3. What does the output indicate?

 

x1   + 2x2 – x3  –  x4 = 1

2x1 +  x2  + x3  –  x4 = 4

x1   -  x2  + 2x3 +  x4 = 7

x1  + 3x2  - 2x3 - 3x4 = 5

 

  1. For the following set of linear equations
    1. Check if the system has a unique solution
    2. Solve the system using Gauss elimination
    3. What does the output indicate?

 

 x1   +  x2 + 3x3  = 1

 x1   + 2x2 + 5x3 = 2

3x1 +  x2  + 5x3 = -1