Which of the following subsets of the vector space r 3 are subspaces of r 3 ?

(i) the set of all vectors v =   x y z   with the property 2xyz = 0.

(ii) the set of all the solutions of the equation x − 5y + 2z = 0.

(iii) the set of all solutions for the system   2 3 2 5 2 8 −1 1 3     x y z   =   0 0 0  .

(iv) the set of all the solutions of the equation x + 3y = 2z + 1.

0,0

step-by-step explanation:

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal

just a girl thing, i think im cute when im not lol