## s3a 2 years ago Basis for the column space of A problem: For #3(a) [ http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/exam-1/MIT18_06SCF11_ex1s.pdf ], how did the solution go from U to R? when c != 3

1. s3a

It seems c was chosen to be 4 but why?

2. ingenuus

divide the second row by (c-3)

3. ingenuus

subtract row2 from row1

4. ingenuus

and so on..

5. ingenuus

c was not chosen to be 4

6. s3a

I get this: http://i.imgur.com/RIZgXlJ.jpg

7. s3a

with what you said

8. ingenuus

good :)

9. s3a

Wait, I think we're miscommunicating. I meant that as in I did what you said and there are still "c"s floating around.

10. ingenuus

well subtract (-4/(c-3))(row3) from row2 and subtract (2+4/(c-3))(row3) from row1

11. ingenuus

i think you should look again row reduced echelon form

12. s3a

but wouldn't that have the position which currently has the leading ones' with "c"s?

13. s3a

Also, sorry for being slow right now, my brain is being overworked and I can't take a break because I have exams.

14. ingenuus

no it won't

15. ingenuus

look at the picture you uploaded

16. ingenuus

row 3 is 1 1

17. s3a

OH!

18. ingenuus

to get the row reduced echelon form, you will make everything zero above pivots right?

19. s3a

Yes, I see it. :D Let me just confirm, I get the same answer.

20. ingenuus

well since row3 is 1 1 it will remove same things above ok i see you got it

21. s3a

I've confirmed that I got it. :D Thanks a lot.

22. s3a

!

23. s3a

"row 3 is 1 1" is what made me see it instantly.

24. s3a

(Just saying.)

25. ingenuus

good luck on your exam! :)

26. s3a

Thanks. :)

27. s3a

(Also, good luck on yours if you have any.)

28. s3a

Actually, I have another question. Why does it matter what c is equal to if it dissapears thanks to elimination? (Sorry if that's a dumb question.)