True or false. If true or false state your reason.
2 lanes are subspaces of R2 because: if we have y=mx and (t, mt)
1. They are closed under addition: (t, mt)+(s, ms)=(t+s, m*(t+s))
2. They are closed under scalar multiplication: r*(t, mt)=(rt, r*(mt))
3. Zero vector because they pass through the center of grid coordinates.
These 2 lanes are isomorphic because for each x there is y1 and y2 (one-to-one).
Similarly, each plane in R3 passing through origin is a subspace and has equation ax+by+cz=0. Both planes isomorphic because they also have one-to-one correspondence between points on the plane
Thank you.
Solution
This is TRUE.....zero vector acts as the identity element....so a plane to be subspaces it need to pass through origin.....in case of y = mx the plane is passing through origin and hence it forms subspaces.....
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True or false- If true or false state your reason- 2 lanes are subspa.docx
1. True or false. If true or false state your reason.
2 lanes are subspaces of R2 because: if we have y=mx and (t, mt)
1. They are closed under addition: (t, mt)+(s, ms)=(t+s, m*(t+s))
2. They are closed under scalar multiplication: r*(t, mt)=(rt, r*(mt))
3. Zero vector because they pass through the center of grid coordinates.
These 2 lanes are isomorphic because for each x there is y1 and y2 (one-to-one).
Similarly, each plane in R3 passing through origin is a subspace and has equation ax+by+cz=0.
Both planes isomorphic because they also have one-to-one correspondence between points on the
plane
Thank you.
Solution
This is TRUE.....zero vector acts as the identity element....so a plane to be subspaces it need to
pass through origin.....in case of y = mx the plane is passing through origin and hence it forms
subspaces.....
