Question

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

Answer 1

It seems c was chosen to be 4 but why?

Answer 2

divide the second row by (c-3)

Answer 3

subtract row2 from row1

Answer 4

and so on..

Answer 5

c was not chosen to be 4

Answer 6

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

Answer 7

with what you said

Answer 8

good :)

Answer 9

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

Answer 10

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

Answer 11

i think you should look again row reduced echelon form

Answer 12

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

Answer 13

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

Answer 14

no it won't

Answer 15

look at the picture you uploaded

Answer 16

row 3 is 1 1

Answer 17

OH!

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

I've confirmed that I got it. :D

Thanks a lot.

Answer 22

!

Answer 23

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

Answer 24

(Just saying.)

Answer 25

good luck on your exam! :)

Answer 26

Thanks. :)

Answer 27

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

Answer 28

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.)