Question: Is the subset P(x,y,z) described by 8x-y+2z=0  a subspace of R3? Why or why not?   Is my interpretation of subspace correct? Are there any explicit theorems that explain this concept? This is what I came up with: The subset P(x,y,z)described by 8x - y + 2z = 0 is a subspace of R3 because the plane passes through the origin which is used as the positional matrix. Any scalar of x,y, or z will equal 0 and this is an example of a special subspace called the null space. The system is consistent and has infinitely many solutions.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Is the subset P(x,y,z) described by 8x-y+2z=0  a subspace of R3? Why or why not?

 

Is my interpretation of subspace correct? Are there any explicit theorems that explain this concept? This is what I came up with:

The subset P(x,y,z)described by

8x - y + 2z = 0

is a subspace of R3 because the plane passes through the origin which is used as the positional matrix. Any scalar of x,y, or z will equal 0 and this is an example of a special subspace called the null space. The system is consistent and has infinitely many solutions.

 

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