## anonymous one year ago A question about linear algebra.... See attachment please

1. anonymous

2. anonymous

My question is...... are there times when you can't express the result as a linear combination of the two others?

3. anonymous

If so is what clues you in on that?

4. ganeshie8

Maybe lets try an example in $$xy$$ plane first : can you express the vector $$(2,2)$$ using a linear combination of vectors $$(1,0)$$ and $$(2,0)$$ ?

5. anonymous

So when you say the vector (2,2) that would be $a_{1}=\left(\begin{matrix}2 \\ 2\end{matrix}\right)$ correct?

6. ganeshie8

right

7. anonymous

ok give me a second to try it out

8. ganeshie8

take ur time

9. anonymous

I can see it now because both of the "Y" elements are zero then there is no multiple of zero that could combine to equal 2

10. anonymous

Thank you, is there a method in general (by inspection) that I can use to check one of these before attempting to work the problem out?

11. ganeshie8

so what do you conclude ?

12. ganeshie8

Yes, there is a method. Before getting to that, I just want to see you get the idea of taking linear combinations of vectors..

13. anonymous

If all X,Y,Z, or Nth element of each vector is zero and the resultant vector is non-zero I can concluded that there is no linear combination of the vectors that will give the correct resultant vector

14. anonymous

And I am not sure i am getting the idea your referring to

15. ganeshie8

I am not referring to any idea yet

16. ganeshie8

The present problem is cooked up to be done by visual inspection

17. anonymous

What I meant is you said " I just want to see you get the idea of taking linear combinations of vectors." and honestly I am not sure that I am

18. ganeshie8

for part (i), try $$3a_1 + 2a_2$$

19. ganeshie8

for part (ii), try $$3a_1 + 4a_2$$

20. anonymous

I actually found a solution for both....

21. anonymous

So I was trying to figure out 1) if there was a time this wouldn't work. (which you have shown me) and a way to inspect them and get a definite "NO" sometimes.... if what I am saying makes sense