Question

Show R^3 =span((1,1,1),(1,1,-1),(-1,1,1))

Answer 1

need to show the three vectors are linearly independent of one another

Answer 2

right and my REEF matrix is
1 0 0
0 1 0
0 0 1
which would tell me this right? because i have no unknown variables?

Answer 3

linearly independance means u reduce
Ax=o matrix

and linear independent matrices only contain the 0 matrix. therefore the three set of vectors span R3 due to linearly in dependancy

Answer 4

hmmm. . . ill have to dig into this more >.< but think it makes sense

Answer 5

so if I have a matrix which ends witha bottom line of say 0 0 0 i know it is dependent on the others too then?

Answer 6

you have known variables... it is just that x=0 y=0 z=0

Answer 7

yea, one vector can be written as a linear combination of the other 2 vectors

Answer 8

right ok i see what your saying now, because yes i did leave out the final cllm which would have been my 0 vector.

Answer 9

yea. that would be ur zero vector, illustration that the only solution the that system would be x=0 y=0 z=0 which is simply the zero vector. and for vectors to be linearly independent then the only solution to the system can only be the zero vector

Answer 10

got it. thx

Answer 11

when u know what to do, u will boss every question

Answer 12

right, and its a condensed summer term class covering 12 weeks of stuff in 7 so we are flying >.< but not much as been getting past me yet . lol

Answer 13

no worries, i'm here if u need anything. i just love linear algebra

Answer 14

well waht ur doing right now

Answer 15

yep. closing this out now but its going fun its just a mind flutter at times with all the rules and tricks and stuff. Hence why i call it crazy math!

Answer 16

yea alot of weird stuff happens, especially when u go over the proofs for this, just gets too hectic

Answer 17

yep and he loves proofs lol.

Answer 18

hahah, that just screws everyone over haah when it comes to examples you are LIKE OHHH I TOTALLY GET IT