I just wanted to know if my answer is acceptable.(adsbygoogle = window.adsbygoogle || []).push({});

Q: S={(x,y,z) E [itex]\mathbb{R}^{3}[/itex] l x^2 + y^2 +z ^2 =0}

Is it a subspace of [itex]\mathbb{R}^{3}[/itex]?

My answer:

It is a subspace if x=0, y =0, z= 0

Let u=(0,0,0) u2=(0,0,0) and k be a scalar

u + u2 = (0,0,0) Closed under addition

ku = k(0,0,0) = (0,0,0) Closed under scalar multiplication

Is my answer complete? I'm not sure if I'm allowed to assume that the values of x,y,z are 0.

Thank you in advance

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# Homework Help: Subspace (question)

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