Question

find the dimension of the set T={(x,y-x,y+z,z)|x,y,z are element of real numbers}

Answer 1

The dimension is basically the number of pieces of information you need to define each member of the set. Each member has a specific x, y and z value, so do you think you can answer the question now?

Answer 2

Think of it this way: to locate a point in 2 dimensional space you need 2 pieces of information (the x and y value) - that is why it is 2 dimensional. Does this help?

Answer 3

from your information i think the dimension is four(4) ....tell me if am wrong

Answer 4

Could you please explain the thinking behind your answer? I don't think it's quite right.

Answer 5

Here's another analogy:
Element x is equal to 1x+0y+0z.
Element y-x is equal to (-1)x+1y+0z.
Element y+z is equal to 0x+1y+1z.
Element z is equal to 0x+0y+1z.

So each element can be properly defined using multiples of x, y and z.
The dimension is how many pieces of information we need to define each element, so the dimension is?

Answer 6

try breaking the vector into distinct peaces, one for each letter (variable)

Answer 7

the dimension is 3 @traxter

Answer 8

Yes very good :) Do you understand the meaning behind it ok?

Answer 9

yes,i understand....the dim=3 ,since we have 3 elements like (1,0,0);(0,1,0);(0,0,1)

Answer 10

Yes exactly. If you're doing linear algebra then technically the dimension is just the number of vectors in the basis.

Answer 11

in my question the dim(T)=3 right? becoz we gonna have x(1,1,0,00)+y(0,1,1,0)+z(0,0,1,1)

Answer 12

Yep :)