(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

P={(x,y,z)|x+2y+z=6}, a plane in R^{3}. P is not a subspace of R^{3}. Why?

2. Relevant equations

See below.

3. The attempt at a solution

I am really quite confused here.

My text says:

"A subset W of a vector space V is called a subspace of V if W is itself a vector space under the addition and scalar multiplication defined on V"

and goes on to say that the only axioms that need verification are:

(a) If u and v are vectors in W, then u+v is in W.

(b) If k is any scalar and u is any vector in W, then ku is in W.

So from here...I'm a bit confused. Where does this x+2y+z=6 come in to play? I'm really quite lost and cannot find any relevant examples in my text.

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# P is not a subspace of R3. Why?

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