Example 1

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Gaussian elimination example

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Example 1

  1. 1. Gaussian Elimination Image from WikiMedia Commons created in LightWave by stib http://commons.wikimedia.org/wiki/File:Secretsharing-3-point.png
  2. 2. Example <ul><li>Solve the system of linear equations using Gaussian elimination. </li></ul>
  3. 3. Example <ul><li>First, we write the augmented matrix. </li></ul>System of equations: Augmented matrix:
  4. 4. Example <ul><li>Now we perform a sequence of elementary row operations to obtain a row-equivalent matrix in row-echelon form. </li></ul>
  5. 5. Example
  6. 6. Example <ul><li>Replace Row 2 with (-2) × Row 1 + Row 2 </li></ul>
  7. 7. Example <ul><li>Replace Row 2 with (-2) × Row 1 + Row 2 </li></ul><ul><li>Replace Row 3 with (-4) × Row 1 + Row 3 </li></ul>
  8. 8. Example <ul><li>Replace Row 2 with (-2) × Row 1 + Row 2 </li></ul><ul><li>Replace Row 3 with (-4) × Row 1 + Row 3 </li></ul><ul><li>Replace Row 3 with ( -3 / 5 ) × Row 2 + Row 3 </li></ul>
  9. 9. Example <ul><li>The augmented matrix is now in row-echelon form. </li></ul>
  10. 10. Example <ul><li>The associated system can be solved by backward substitution. </li></ul><ul><li>The solution is (1, 0, 1). </li></ul>System of equations: Augmented matrix:

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