(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What are the intersections of the following pairs of subspaces?

(a) The x-y plane and the y-z plane in R'.

(b) The line through (1, 1, 1) and the plane through (1,0, 0) and (0, 1, 1).

(c) The zero vector and the whole space R'.

(d) The plane S perpendicular to (1, 1, 0) and perpendicular to (0, 1, I) in R3

What are the sums of those pairs of subspaces?

2. Relevant equations

3. The attempt at a solution

So I've been using logic, but I don't know if what I'm doing is right or makes sense...

a) I think the intersection is the y-axis (it's where the two planes I believe meet). And for the sum I have that R^{3}= x-axis + y-axis+z-axis that can be written as a combination of a member of the xy- and yz-planes. So, R^{3}=xy-plane_yz-plane

b) In 3D, a line is either parallel to a plane or intersects it in a single point. So, I'm thinking it should intersect at the single point (1,1,1) and that the sum should be the plane through (1,0,0) and (0,1,1), but I'm a bit at a loss here...

c) The intersection I think should be the lonely zero vector and their sum I think is the whole space R^{3}.

d) This one I'm completely lost!

Can anyone please help me, particularly with parts B and D, and let me know if my logic seems right?

Thanks!!!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Finding intersection of vector subspaces

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