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My book says it is zero, but I don't know where to start , why is it zero ? I have to take an exam in few hours :cry: so a simple explanation would be appreciated ( I'm not studying pure physics:smile: Here are the electric fields of the three regions . Thanks in advance :smile:

Homework Statement Hi , in the first chapters of my physics book states that positive charges don't move , but now this new chapter about curruent and resistance says that the direction of the current is the direction in which the positive charges flow or move . I'm confused :confused: Can...

Let ##L## be a linear operator ::##L(A)= Tr(A)## where ##Tr(A)## is the trace of a square matrix Find a basis of the kernel of L. Any help would be really appreciated . thanks in advance

Thanks :smile:

Thanks but why ##O=L(aA+bB)=aL(A)##?? could you please explain what they do there, please??

Homework Statement Let ##L: R^{2} → R^{2}## be a linear map such that ##L ≠ O## but## L^{2} = L \circ L = O.## Show that there exists a basis {##A##, ##B##} of ##R^{2}## such that: ##L(A) = B## and ##L(B) = O.## The Attempt at a Solution Here's the...

It makes sense now ,thanks .

You are right !:smile: could you explain please why ## L\circ(-L-2)=-L^{2}-2L## ?? if "2" was a linear mapping then the properties would work for this, right? but 2 is a scalar.

Ok so ##L^{-1}I = L^{-1}L(-L-2)## yields ##I \circ (-L-2)=-L-2## right ?? . Thanks

Hmm I guess there's something that's still not clear for me , the first property of composition you wrote works for three linear mappings right?, but in this case we have two linear mappings and a number :L°(-L-2) I know I'm wrong somewhere but I don't know where ,I'm confused :confused: .Any...

ok , I see .Thank you very much :smile:

hmm ok you mean I=L(-L-2) but can you operate with L^2 like it was a number?? , isn't L^2 =L°L ?? I'm confused:confused:

hmm ,that doesn't tell me anything :confused:

Homework Statement Let L: V →V be a linear mapping such that L^2+2L+I=0, show that L is invertible (I is the identity mapping) I have no idea how to solve this problem or how to start,I mean this problem is different from the ones I solved before, the answer is "The inverse of L is -L-2 "...

Thank you so much HallsofIvy , I understood all your explanation . It's cool to know that there's still good people who like to help others .Greetings from Chile

Homework Statement Hi guys , I have this problem ,well actually I don't understand the solution they provide , Here's the problem statement and the solution . May someone please explain the solution to me?? Thanks so much, Sorry for my bad english Homework Equations 1.I understand...