Question

Find bases for the four fundamental subspaces of the Matrix A. V1=(1,0,2),V2=(1,1,0),V3=(-1,0,-1) Need answer Find bases for the four fundamental subspaces of the Matrix A. V1=(1,0,2),V2=(1,1,0),V3=(-1,0,-1) Need answer @Mathematics

Answer 1

just so you don't get the matrix messed up, those are column vectors. I'm not sure how to put in a 3x3 matrix

Answer 2

for Rank, did you basically get the standard basis for R3?

Answer 3

well you can see they are all dependent so it could be the originals vectors but i like nicer numbers

Answer 4

I think you mean to say independent

Answer 5

\[R(A^T)=(1,0,0)^T,(0,1,0)^T,(0,0,1)^T\] and i mean't columnspace

Answer 6

You cannot write the other vectors in the form of others therefore they're all dependent

Answer 7

you have dependent and independent backwards

Answer 8

We just went over some of this stuff tonight in Linear Algebra... not far enough along yet to answer your questions, but I can help with the matrix... if they are column vectors, the matrix should be:

[ 1 1 -1 ]
[ 0 1 0 ]
[ 2 0 -1 ]

Answer 9

ahh yeah i just noticed that

Answer 10

I thought I was going to be able to do that with the editor but it didn't work, but that should work, but I just saw you meant column space, so I guess that's not what you meant anyway :P

Answer 11

\[\left[\begin{matrix}1 & 1&-1 \\0 & 1&0 \\ 2 & 0&-1 \end{matrix}\right]\]

Answer 12

right click on my matrix and view source to see what I did.

Answer 13

'show source'

Answer 14

so did you get the same for the transpose of the columnspace and the columnspace

Answer 15

are you looking for a basis for A and A transpose?

Answer 16

Its Zarkon! awesome :)

Answer 17

Hi joe :)

Answer 18

i'm looking for the four fundamentals, so the Column spaces and nullspaces of Matrix A and it's transpose

Answer 19

it is me

Answer 20

awesome!

Answer 21

the matrix has full rank (and it is square) so the null space is just the zero vector

Answer 22

yeah that's what i was assuming but you got the standards for the column spaces?

Answer 23

The the null space of A transpose will also be just the 0 vector, as the rank of A is the same as the rank of A transpose.

Answer 24

use the originals if you want

Answer 25

they are L.I.

Answer 26

So this problem is that bad. All the columns form a basis for the Col Space, all the rows form a basis for the Row Space, and the Null Space and Left Null Space are trivial.

Answer 27

isnt* i meant isnt >.> lol

Answer 28

That's why i asked for the answers lolz XD it's on my pretest that my teacher gives no answers