Thread: Showing two subspaces are a direct sum

Consider the subspaces S1={(r,0,t): r,t∈R} and S2={(s,s,0): s∈R} of R^3. Prove that S1⊕S2=R^3.

I am not sure how to show this at all, my teacher didn't give us any examples of this. Would really appreciate some help please.

Originally Posted by steph3824

Consider the subspaces S1={(r,0,t): r,t∈R} and S2={(s,s,0): s∈R} of R^3. Prove that S1⊕S2=R^3.

I am not sure how to show this at all, my teacher didn't give us any examples of this. Would really appreciate some help please.

Prove that every vector can be written as sum of vector from and vector from in an unique way.

And it's clear that


These two things will give you