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Is the subset a subspace of R3? If so, then prove it. If not, then give a reason why it is not. The vectors (b1, b2, b3) that satisfy b3- b2 + 3B1 = 0

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My notation of a letter with a number to the right, (b1) represents b sub 1.

Im having a problem on how far I need to go to show this is a subspace.

I know that since the equation that I am given is homogenous, the vector

(0,0,0) is included and it passes through the origin.

There is an example in my book where they say that because the (0,0,0) is not included it is enough to show it is not a subspace.

I know the test if u and v are vectors and

u and v are in W then u + v is in W

and if u is in W and c is any scalar, then cu is in W.

Do I need to use this test? or is the origin enough to be proof?

If the test is needed can someone bumb me in the direction of where to start this proof?