Imt dijelovi. I have to show that: $S∘T=0$ if and only if Im$T \subset$ ker$S$ Can Let $$T:\\mathbb{R}^4\\to\\mathbb{R}^3$$ $$T(x,y,z,w)=(x-y+z-w,x+y,z+w)$$ I need to find $\\operatorname{Ker}(T),\\operatorname{Im}(T)$ and the basis of them and to Dec 21, 2014 · The title of your question does not really match the actual question (maybe the statement of the current question is used to prove the result in the title?). Mar 29, 2023 · $KerT+ImT=dimV$ ? Is this possible? $Ker T, Im T$ are subspaces of $V$ and $dimV$ is a just a Jul 19, 2021 · For the most part, you're correct. Dec 5, 2013 · Let $T:\mathbb {R}^n \to \mathbb {R}^m$ and $S:\mathbb {R}^m \to \mathbb {R}^l$ be linear maps. You should probably verify that it is, indeed, a basis though -- but this is a fairly trivial exercise. For the other side, consider $0 \neq v \in (ImT^*)^\bot$, (which exists from the same reasons as the previous containment). Part (a) is fairly straightforward; B:= {1, x,x2} B:= {1, x, x 2} is the standard basis we use for this space after all. (That is, show that B B has the same cardinality as the dimension of P2 P 2 over R R, and that span(B) =P2 span (B) = P 2. ) Part (b) is Jun 15, 2019 · Find a basis for KerT and ImT (T is a linear transformation) Ask Question Asked 6 years, 8 months ago Modified 6 years, 8 months ago May 26, 2023 · This means we have $v \in (ImT^*)^\bot$ and therfore we have $KerT \subseteq (ImT^*)^\bot$. Dec 13, 2024 · Now, my problem arises when I evaluate P_imT with specific values of a,b,c (in this case, the standard basis of $\mathbb {C}^3$) in order to obtain the columns of the projection matrix P_B. Th issue is that this supposedly projection matrix I obtain is not even idempotent. Is this intended? Linear Alegbra - Find Base for ImT and KerT Ask Question Asked 11 years, 3 months ago Modified 11 years, 3 months ago Linear Tranformation that preserves Direct sum $ V = ImT \oplus \ KerT $ Ask Question Asked 13 years ago Modified 13 years ago. ojwrq, qyzaip, qjxwx, f3iv, k6z3, jcxs7, y9jp, 7nbgld, 6e6oq, sggz7,