Question

Help with proving W = (1,2,4x+3Y) not a vector

Answer 1

are there any more details to this question?

Answer 2

x and y are real numbers and V = R3

Answer 3

Help with proving W = (1x,2y,4x+3Y) not a vector , x and y are real numbers and V = R3

Answer 4

not a vector or not a vector space?

Answer 5

not a vector sub space

Answer 6

okay, makes more sense now

Answer 7

it appears to pass the conditions to be a subspace of R^3

Answer 8

how to prove with addition

Answer 9

Let \[\vec{a}=(x_1,2y_2,4x_1+3y_1)\] and \[\vec{b}=(x_2,y_2,4x_2+3y_2)\] be in W

Answer 10

Now \[\vec{a}+\vec{b}=(x_1+x_2,y_1+y_2,4x_1+3y_1+4x_2+3y_2)\]
group and factor the third component to get \[(x_1+x_2,y_1+y_2,4(x_1+x_2)+3(y_1+y_2))\]

Answer 11

since \[x_1,x_2,y_1,y_2\in \mathbb{R}\]

clearly this vector sum of arbitrary vectors in W is in W

Answer 12

I should have made the statement about \[x_1,x_2,y_1,y_2\in \mathbb{R}\] first of course

Answer 13

Thank you I am reviewing to make sure I understand.

Answer 14

would it work the same if W = x,2y,4x - 3Y

Answer 15

it should, but I have not tried it, Proving a subspace is one of those "turn the crank" type proofs in linear algebra that may seem a little abstract at first but once yo get the process down is straight forward but sometimes tedious...

Answer 16

Thank You

Answer 17

IS W subspace of V, W is the set of all functions
F(0)=1 , V=C(\[-\infty\],\[\infty\])