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How to determine whether a given set of vectors SPANS R 3

How to determine whether a given set of vectors SPANS R 3. example 1: This set does SPAN R 3. example 2: This set does NOT SPAN R 3. Do solutions exist for all x, y, and z ?. Do solutions exist for all x, y, and z ?. Do solutions exist for all x, y, and z ?.

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How to determine whether a given set of vectors SPANS R 3

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  1. How to determine whether a given set of vectors SPANS R3 example 1: This set does SPAN R 3 example 2: This set does NOT SPAN R 3

  2. Do solutions exist for allx, y, and z ?

  3. Do solutions exist for allx, y, and z ?

  4. Do solutions exist for allx, y, and z ?

  5. Do solutions exist for allx, y, and z ?

  6. 1 1 1 x-y -1 Do solutions exist for allx, y, and z ?

  7. 1 1 1 x-y -1 -1 0 0 1 z-(x-y) Do solutions exist for allx, y, and z ?

  8. 1 1 1 x-y -1 -1 0 0 1 z-(x-y) -1 0 1 2 y-(x-y) Do solutions exist for allx, y, and z ?

  9. 1 1 1 x-y -1 -1 0 0 1 z-(x-y) (x-y)-(2y-x) 0 -1 -1 0 1 2 y-(x-y) -1 Do solutions exist for allx, y, and z ?

  10. 1 1 1 x-y -1 -1 0 0 1 z-(x-y) (x-y)-(2y-x) 0 -1 -1 0 1 2 y-(x-y) -1 (2x-3y)+(z-(x-y)) 0 +1 Do solutions exist for allx, y, and z ?

  11. 1 1 1 x-y -1 -1 0 0 1 z-(x-y) (x-y)-(2y-x) 0 -1 -1 0 1 2 y-(x-y) -1 0 (2y-x)-2(z-(x-y)) -2 Do solutions exist for allx, y, and z ?

  12. 1 1 1 x-y -1 -1 0 0 1 z-(x-y) (x-y)-(2y-x) 0 -1 -1 0 1 2 y-(x-y) -1 Do solutions exist for allx, y, and z ?

  13. 1 1 1 x-y -1 -1 0 0 1 z-(x-y) (x-y)-(2y-x) 0 -1 -1 0 1 2 y-(x-y) -1 = c1 c2 = c3 = YES Do solutions exist for allx, y, and z ?

  14. YES return to outline = c1 c2 = c3 = YES Do solutions exist for allx, y, and z ?

  15. Do solutions exist for allx, y, and z ?

  16. Do solutions exist for allx, y, and z ?

  17. Do solutions exist for allx, y, and z ?

  18. Do solutions exist for allx, y, and z ?

  19. 1 1 1 x-y -1 Do solutions exist for allx, y, and z ?

  20. 1 1 1 x-y -1 -1 0 0 0 z-(x-y) Do solutions exist for allx, y, and z ?

  21. 1 1 1 x-y -1 -1 0 0 0 z-(x-y) There are no solutions if z – x + y does not equal zero Do solutions exist for allx, y, and z ?

  22. 1 1 1 x-y -1 -1 0 0 0 z-(x-y) There are no solutions if z – x + y does not equal zero The set does Not span R3 Do solutions exist for allx, y, and z ?

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