Question

Is the set W-{(x_1,x_2,x_3) R^3: x_1,x_2,x_3 are integers} a subspace of R^3?

Answer 1

W=*

Answer 2

I don't see why not, even if they are all zero, the zero vector is in R3
(R3 has 8 dimensions,1 of1,3 of 1,3 of 2 and 1 of 3).

Also adding it to any other 3 vector or multiplying it by a scalar will also result in a 3vector, member of the same space.

Answer 3

Wrong I got this wrong my midterm, the answer is no b/c it's not closed under multiplication.. I don't know why though..

Answer 4

The answer key says for example v=(1,1,1) but 1/2V = (1/2,1/2,1/)2?

Answer 5

Oh, Ok, restricting to integers..duh.

What a dumb question.

Answer 6

? Still don't get it what do you mean?

Answer 7

In general it's pretty obvious that all the 3 vectors are in a subspace, but not if u restrict them to integer values (which nobody would actually do in practice but I guess it keeps the theoreticians and tutors happy).

Answer 8

oh okay yeah trick questions dammit

Answer 9

Yup:-(

Answer 10

Hey if it's restricted to integer values isn't that everything, like all real numbers?