Question

Linear Algebra Problem.
Help Please!

Answer 1

I'm on it!

Answer 2

Sorry Im having trouble typing it

Answer 3

Ill just post a pic

Answer 4

In the equation editor at the bottom right button you will be able to bring up the matrices and vectors. Or take a picture or draw it. Whatever works!

Answer 5

Number two is the one I am stuck on

Answer 6

It says to prove it if it is a subspace

Answer 7

Do you know what you have to do to prove that it is a subspace?

Answer 8

Yes, check to see if scalar multiplication and vector addition works, but since x_2=x_3 I;m not really sure what to do in that case

Answer 9

normally I sub in the given value but in this cases I would have a set with repeating variables

Answer 10

Well does having a linearly dependent set of vectors matter to if it's a subspace or not?

Answer 11

I guess I am just confused on how I write this out.

Answer 12

Well you have n vectors, but if it was a true subspace of R^n then you'd be able to get to every point in R^n right? So show a vector that isn't a linear combination of x1 and x2.

Answer 13

Think about what a general vector in this space would look like.

for example say any general vector is (a b c)

in this space we know x2 = x3 so a general vector in this space would be (a b b)

so you take vectors of this form and see if scalar multiplication and vector addition works, ie if when u apply scalar multiplication and vector addition, you get back a vector which x2 = x3

Answer 14

So I can right it in that form? I thought repeating variables weren't allowed in set notation, which would change the vector from (a,b,b) to (a,b)

Answer 15

This isn't set notation, this is an element of a vector space

you are right in saying that {a, b, b} = {a, b} which are sets

but this is (a b b), notice the different brackets and also no commas, they are 2 different things

Answer 16

Oh I see, so would I just go through this problem Like I normally would: see if the 0 vector is an element of vector w, scalar multiplication, and vector addition?

Answer 17

Those three requirements must be fulfilled in order for W to be a subspace of R^n, right? That would be the proof?

Answer 18

Correct, good luck :)

Answer 19

Thanks!