## anonymous 4 years ago Find the linear combination of the vectors

1. anonymous

question #50

2. amistre64

augment and rref

3. anonymous

ya but it is becoming an ugly anser

4. amistre64

|its spose to, these things are never pretty :)

5. amistre64

can you type up the first one for me, i have trouble trying to switch back and forth and keep things in order

6. amistre64

A:= u1 u2 u3 Ax = v x = A-1 v = | A | v|

7. anonymous

what do u mean?

8. amistre64

give me the u1 u2 u3 and v so that i can work with them; or else im sure to botch it up between switching back and forth from here to there

9. anonymous

ok will do

10. anonymous

u1= (1,3,2,1) u2=(2,-2,-5,4) u3= (2,-1,3,6) v= (2,5,-4,0)

11. amistre64

$\begin{pmatrix}u_1&u_2&u_3\\1&2&2\\3&-2&-1\\2&-5&3\\1&4&6\\\end{pmatrix}\begin{pmatrix}x\\x_1\\x_2\\x_3\\x_4\end{pmatrix}=\begin{pmatrix}v\\2\\5\\-4\\0\end{pmatrix}$ $\begin{pmatrix}x\\x_1\\x_2\\x_3\\x_4\end{pmatrix}=RREF\begin{pmatrix}u_1&u_2&u_3&|&v\\1&2&2&|&2\\3&-2&-1&|&5\\2&-5&3&|&-4\\1&4&6&|&0\\\end{pmatrix}$

12. amistre64

thats what I mean; but wolfram make light work of it :)

13. anonymous

ummm y did you add the the u1 u2 and u3 ontop?

14. anonymous

Is that part of the matrix

15. amistre64

just to clairify what was what; its not part of the actual process tho, just references

16. anonymous

ohhhh ok i see

17. amistre64
18. anonymous

Thanks amistre :D

19. anonymous

LOL u were born in the same yr as my mom LOL

20. amistre64

and my x vector is one component to many :)

21. amistre64

what year was I born :)

22. anonymous

1964

23. amistre64

nope .... thats just an old aol thing thats stuck with me thru the years :)

24. anonymous

hehe

25. amistre64

so, according to the rref on the wolf: x = <2,1,-1>

26. anonymous

yup i see thanks amistre

27. amistre64

youre welcome; and i was born in 1972 ;) or so ive been led to believe

28. anonymous

hehe so you are not much younger than my mom :D