Solve a system of linear equations

1. Solve a system of linear equations By reducing a matrix Pamela Leutwyler

2. Describe the solutions to:

3. Describe the solutions to: The coefficient matrix:

5. Replace row 1 with row 1 – row 2

6. Replace row 1 with row 1 – row 2 1 1 0 1 -1

8. Replace row 2 with row 2 – row 1

9. Replace row 2 with row 2 – row 1 -1

10. Replace row 2 with row 2 – row 1 -1 0 1 1 0

12. Replace row 3 with row 3 – 3  row 1

13. Replace row 3 with row 3 – 3  row 1 -3

14. Replace row 3 with row 3 – 3  row 1 -3 0 1 1 0

16. Replace row 3 with row 3 – row 2

17. Replace row 3 with row 3 – row 2 -1

18. Replace row 3 with row 3 – row 2 -1 0 0

20. Replace row 1 with row 1 – row 2

21. Replace row 1 with row 1 – row 2 -1

22. Replace row 1 with row 1 – row 2 0 -1 -1

24. The matrix is in REDUCED ECHELON FORM

25. The matrix is in REDUCED ECHELON FORM 1 1 Every FNZE is a 1 First NonZero Entry in a row of a matrix

26. The matrix is in REDUCED ECHELON FORM 1 1 Every FNZE is a 1 Every FNZE is to the right of the FNZE above it.

27. The matrix is in REDUCED ECHELON FORM 0 1 0 1 0 0 Every FNZE is a 1 Every FNZE is to the right of the FNZE above it. In a column containing a FNZE, every other element is a 0

28. Interpret :

29. Interpret : w= -x +z

30. Interpret : w= -x +z y= -z

31. Interpret : w= -x +z y= -z

32. Interpret : w= -x +z x= x y= -z z= z x and z are the independent variables

33. Interpret : w= -x +z x= x y= -z z= z

34. Interpret : Every solution is a linear combination of these vectors