Which of the subsets of R3 is a subspace of R3?(a) W =

Chapter 4, Problem 4.25

(choose chapter or problem)

Which of the subsets of \(R^{3}\) is a subspace of \(R^{3}\)?

(a) \(W=\left\{\left(x_{1}, x_{2}, x_{3}\right): x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=0\right\}\)

(b) \(W=\left\{\left(x_{1}, x_{2}, x_{3}\right): x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=1\right\}\)

Text Transcription:

R^3

R^3

W={(x_1, x_2, x_3): x_1 ^2 +x_2 ^2 +x_3 ^2 =0}

W={(x_1, x_2, x_3): x_1 ^2 +x_2 ^2 +x_3 ^2 =1}