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

2. Describe the solutions to:

3. The coefficient matrix:

5. Replace row 1 with row 1 – row 2

6. 1 110

8. Replace row 2 with row 2 – row 1

10. Replace row 2 with row 2 – row 1 0 011

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

13. -3

14. Replace row 3 with row 3 – 3  row 1 -3 0 011

16. Replace row 3 with row 3 – row 2

18. Replace row 3 with row 3 – row 2 00

20. Replace row 1 with row 1 – row 2

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

24. The matrix is in REDUCED ECHELON FORM

25. 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 1 1 Every FNZE is a 1 Every FNZE is to the right of the FNZE above it. 0 0 0 0 In a column containing a FNZE, every other element is a 0

28. Interpret :

29. w= -x +z

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

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

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

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

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