Is W is a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that apply.) W = {(x1, x2, x3, 0):

Question

Is W is a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that apply.)
W = {(x1, x2, x3, 0): x1, x2, and x3 are real numbers}
V = R4

A) W is a subspace of V.

B) W is not a subspace of V because it is not closed under addition.

C) W is not a subspace of V because it is not closed under scalar multiplication.

in progress 0
Arya 4 months 2021-10-08T13:25:21+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-08T13:27:11+00:00

    Answer:

    A) W is a sub space of V

    Step-by-step explanation:

    given that V=R^4 and W= [(x_1,x_2,x_3,0)|x_1,x_2,x_3E..R]

    W is a subspace of V because of the follwing.

    let (x_1,x_2,x_3,0),(y_1,y_2,y_3,0)W and a,bV

    now a(x_1,x_2,x_3,0)+b(y_1,y_2,y_3,0)= (ax_1, ax_2,ax_3,0)+(by_1, by_2,by_3, 0)\\\\=(ax_1, +by_1,ax_2+by_2,ax_3,+by_3,0+0)=(ax_1+by_1, ax_2+by_2,ax_3, +by_3,0)W

    since ax_1 +by_1,ax_2 ,+by_2,ax_3+by_3 are all elements of R

    W is closed under vector adiition and scalar multiplication.

    Hence W is a sub space of V.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )