Question

consider the natural basis for R4,and let W be spanned by {(1,-1,2,-3)(1,1,2,0)(3,-1,6,-6)}
find the standard basis for W

Answer 1

check P75 in the guide,

Answer 2

If someone helps me then I will help them!

Answer 3

@HorseCrazyGirlForever what kind of help do u want???

Answer 4

Help with a measuring problem I just bumped my question.

Answer 5

just row reduce the vectors and it will produce the standard vectors

Answer 6

@matrix65 ......dnt hav a guide....just cut it and paste it here or email me on.......

Answer 7

@amistre64 how??

Answer 8

how to row reduce?

Answer 9

row reduce is like chapter 1, basis is material that uses row reductions.

Answer 10

http://www.wolframalpha.com/input/?i=rref+%7B%7B1%2C1%2C3%7D%2C%7B-1%2C1%2C-1%7D%2C%7B2%2C2%2C6%7D%2C%7B-3%2C0%2C6%7D%7D `

Answer 11

that cant help..... that wont be a basis....@amistre64

Answer 12

solution,..lol
write the vectors in the spanning set as rows of a matrix:
1 -1 2 -3
1 1 2 0
3 -1 6 -6

reduced to Hermine normal form gives
1 0 2 -3/2
0 1 0 3/2
0 0 0 0
then a standard basis for W is given by the rows of the matrix
i.e {(1;0;2;-3/2),(0;1;0;3/2)} is a standard basis for W w.r.t the natural basis for R4.
NB: dim W=2

Answer 13

if you take the three vectors, and augment them next to each of the standard R4 vectors, you can determine if the standard R4s can be created by the given vectors.

Answer 14

@matrix65 gona nje.....r u done

Answer 15

@msamido wat tym r we writing linear algebra, lol dats the ansa, wat else do u want. hahaha ga se nna ke guide ya Mr.T

Answer 16

Wx=[1,0,0,0], if x = (W|[1,0,0,0]) has a solution.

http://www.wolframalpha.com/input/?i=rref%7B%7B1%2C1%2C3%2C1%7D%2C%7B-1%2C1%2C-1%2C0%7D%2C%7B2%2C2%2C6%2C0%7D%2C%7B-3%2C0%2C6%2C0%7D%7D

[1,0,0,0] cannot be formed and so is not in the span, nor can be used to produce any vector in W

i believe 0,1,0,0 and 0,0,0,1 are the only 2 that are usable

but then again, its been awhile since i tried working out this stuff :)

Answer 17

@amistre64 they used Hermite's normal form method to reduce the matrix

Answer 18

@matrix65 ...im not writtin ...thats y im stress less but u gonna write 14h00 on mondy

Answer 19

then im sure the hermite will be effective ;)

Answer 20

@amistre64
im gettin lost

Answer 21

im not soo sure that I aint lost meself

Answer 22

@matrix65 i 4gotten it just remmbr me a lil bit

Answer 23

@msamido y u nt writing, lol stop joking please!

Answer 24

im not .... but plz dnt tell any 1 coz im pretenting tht im writtin ...gore ke maizixe

Answer 25

hahahaha lol people qualified with disdinctions, 98%,

Answer 26

dnt tell any 1 plz it mst remain a c-cret between us

Answer 27

i'll ckeck 2day ko notice board,lol i know ur student number*hides*

Answer 28

wr dd u got my std no??