Question

What's a vector space?

Answer 1

the space where maths works,
ie you can do algebra with vectors in this space

Answer 2

What would be considered a space where can don't math? Where we can't do algebra with vectors?

Answer 3

that would not be a vector space

Answer 4

Can you give me an example of a vector space ?

Answer 5

if you have a space where vectors are \[(x,y,1)\]
adding two vectors together takes you out of the space
\[(x_1, y_1,1)+(x_2, y_2,1)=(x_1+x_2,y_1+y_2,2)\] which is not in the same space (the third component is 2 not 1,
therefore \[(x,y,1)\] is not a vector space

Answer 6

is \[(x,y,z)=(x,y,0)\] a vector space?

Answer 7

you have to prove the space is closed under addition scaler multiplication and some other rules that define a vectror space

Answer 8

\[(x,y,0)\]is a vector space by the way

Answer 9

3 properties must hold
1) O vector lies in the space
2) for all x,y in the space, the defined sum (x+y) must be also in the space
3) for all x in the space, k is real number, the vector kx is also in the space.

Hope this helps.

Answer 10

Adding two vectors regardless of what the vectors are takes you out of the vector space?

Answer 11

2 vectors you are using must be in the space first.

Answer 12

Oh I get it kinda. Basically think of vector space as a box and vectors as lines. If two long lines take you out of the box then adding those two vectors takes you out of the vector space?

Answer 13

yup

Answer 14

What's a physical representation of the zero vector and can you give an example of when it will not lie in a vector space?

Answer 15

It must lie in the vector space, otherwise, the vector space is empty ( which is not good)

Answer 16

Look at the example of UnkleRhaukus, (0,0,0) is in the vector space (Check it out!)

Answer 17

Ok now I get it thanks everyone!!