Question

Consider the plane P = \begin{Bmatrix} \mathbf{v} = \begin{pmatrix} x \ y \ z \end{pmatrix} \in \mathbb{R}^3 : 3x - y + 2z = 1 \end{Bmatrix} It meets the x-axis at the point 1/3 1 It meets the y-axis at the point and it meets the z-axis at point 1/2 Does it also pass though the origin? No. Note: enter points using the Maple notation, e.g. [1, 2, 3]. This subset P of $\mathbb{R}^3$ is [select all that apply]: also a subspace of $\mathbb{R}^3$ by the subspace theorem not a subspace of $\mathbb{R}^3$ because it is empty not a subspace of $\mathbb{R}^3$ because it is not closed under scalar multiplication not a subspace of $\mathbb{R}^3$ because it is not closed under vector addition not a subspace of $\mathbb{R}^3$ because it doesn't contain the zero vector of $\mathbb{R}^3

          Consider the plane
P = \begin{Bmatrix} \mathbf{v} = \begin{pmatrix} x \ y \ z \end{pmatrix} \in \mathbb{R}^3 : 3x - y + 2z = 1 \end{Bmatrix}
It meets the x-axis at the point 1/3
1
It meets the y-axis at the point
and it meets the z-axis at point 1/2
Does it also
pass though the origin? No.
Note: enter points using the Maple notation, e.g. [1, 2, 3].
This subset P of $\mathbb{R}^3$ is [select all that apply]:
also a subspace of $\mathbb{R}^3$ by the subspace theorem
not a subspace of $\mathbb{R}^3$ because it is empty
not a subspace of $\mathbb{R}^3$ because it is not closed under scalar multiplication
not a subspace of $\mathbb{R}^3$ because it is not closed under vector addition
not a subspace of $\mathbb{R}^3$ because it doesn't contain the zero vector of $\mathbb{R}^3

Consider the plane
P = 𝐯 =
< p m a t r i x >
∈ℝ^3 : 3x - y + 2z = 1
It meets the x-axis at the point 1/3
1
It meets the y-axis at the point
and it meets the z-axis at point 1/2
Does it also
pass though the origin? No.
Note: enter points using the Maple notation, e.g. [1, 2, 3].
This subset P of ℝ^3 is [select all that apply]:
also a subspace of ℝ^3 by the subspace theorem
not a subspace of ℝ^3 because it is empty
not a subspace of ℝ^3 because it is not closed under scalar multiplication
not a subspace of ℝ^3 because it is not closed under vector addition
not a subspace of ℝ^3 because it doesn't contain the zero vector of ℝ^3

Added by Aitor T.

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