## atjari 3 years ago For three vectors to form a spanning set whether they should be linearly dependent or independent?

1. atjari

Pls sum1 help

2. amistre64

is a panning set "the most efficient" set?

3. amistre64

if so, then all vectors of an efficient span should be INd

4. atjari

I had a question asking to prove that a particular vector is not in the space spanned by other two vectors out of the three vectors given. Hw do I do that.

5. amistre64

3 vectors with 3 components right?

6. atjari

ya

7. amistre64

there is a thrm in the book; got no idea which number for you;yas that if the rref matrix ov the vectors has a pivot in every row; then they are INd and you cannot create any particular vectorfrom a linear combonation of the other 2

8. amistre64

in other words: 1 0 0 0 1 0 is the rref then you have INd vectors that cannot be created from the 0 0 1 other 2

9. amistre64

i spose rref imight be a little further than needed to go; as long as there is a pivot in each row regardless you are good to go

10. atjari

What do you mean by pivot here?

11. amistre64

pivot is a matrix term for .... well ... a leading number in a row that aint a zero

12. amistre64

0034 3 is the pivot point

13. amistre64

512 5 is your pivot point 002057 2 is your pivot point

14. atjari

Sorry I am nt very thorough with matrix cos I'v nt finishd learning yet. If I am to prove that I should show that the determinent is not equal to zero. Am I right?

15. amistre64

determinate not=0 is prof enough in my book

16. amistre64

10 01 det = 1 ; not zero; these are the vectors for the xy plane 12 48 det = 0 since they are the same vector; can be made from a linear combonation of the others

17. atjari

Thanx a lot. If u dnt mind shall I ask u a question.

18. amistre64

yeah, at my age we dont really have a grade :) maybe the 35th or so