Question

Linear Algebra help!

Answer 1

Determine which of the following subsets of \[\mathbb{R} ^{n}\] are in fact subspaces of \[\mathbb{R} ^{n}\] (n>2).

Answer 2

\[\left\{ x|Ax=b, where A _{m*n} \neq0 and b _{m*1}\neq0 \right\}\]

Answer 3

SOMEBODY HELP!!!

Answer 4

http://www.twiddla.com/563373

Answer 5

saifoo that doesn't show anything..

Answer 6

now>

Answer 7

I asked if:
{x| Ax=b, where A is not a 0 matrix and b is not a 0 column}
was a subset of R^n

Answer 8

Take R3, you have 8 dimensions, 1 subspace of 0-dim, 3 of 1-dim, 3 of 2-dim and 1 of 3-dim.

In general for Rn, total dim = 2^n

Maybe that helps?

Answer 9

No my point is.. is this set:
S = {x|Ax=b, where A is a non-zero matrix and b is a non-zero column} a subspace of R^n?

I have to use the proof, you know the sum must belong in the set and the multiplication by a scalar must belong in the set too..

Answer 10

Square matrices?

Answer 11

No, I wrote A is m by n and column b is m by 1

Answer 12

a bit higher up..like 3 post

Answer 13

Is m > n?

Answer 14

not necessarily.. A is just a matrix with m rows and n columns... b is a column...

Answer 15

m and n are just any numbers of rows and columns..

Answer 16

So in R3, say, A could be a (any number) by 3 matrix?

Answer 17

okay nevermind, I got the answer.. this is how if you are interested:
Suppose S = {x|Ax=b, where A is any non-zero matrix and b is any non-zero column}, or
S is the solution set to the system Ax=b

Answer 18

Suppose x1 and x2 (x sub 1 and x sub 2) are solutions to Ax=b, then
A x1 = b
A x2 = b
Now let (x1 + x2) = x3

Answer 19

If S is a subspace, then A x3 = b too, but

A x1 + A x2 = b + b = A (x1+x2) = A x3 = 2b

Answer 20

2b is not equal to b, unless b=0, therefore this is not a subspace..

Answer 21

I deserve a good answer too xD, but thanks for the effort estudier ..

Answer 22

actually i have one more question..

Answer 23

I will have to chew on that for a bit, I'm not sure that I follow...

Answer 24

Are non-singular matrices subspaces?
What this means is, if I add two non-singular matrices of the same size, will the sum be non-singular
and if I multiply a nonsingular matrix by a scalar is the result non-singular as well?
Size can be anything..

Answer 25

I am more accustomed to treating Rn as a vector space and matrices just as vector representations.

Answer 26

I think I got this now, your b is in Rm.

If Ax = b is solved by a particular solution p, then your solution set is all vectors equal to p + v, where v is is a solution of Ax = 0.