Please help me solve this
A transformation T on vector ? of a vector space is defined by T (v ) = A x ? Where the given vector A W and x means the vector product. Find (T2 + A2 T ) ( V ).
4.10. Let T be a linear transformation on a vector space V satisfying T-T2 = id. Show that T is invertible.
W is a rele that A linear transformation T from a vector space V into a vector space assigns to each vector 2 in V a unique vector T() in W. such that (1) Tutu = Tu+Tv for all uv in V, and (2) Tſcu)=cT(u) for all u in V and all scalar c. *** The kernel of T = {UE V , T(U)=0} The range of T = {T(U) EW , ue V } Define T :P, - R...
Find an example of a vector space V, and a linear transformation T : V + V such that R(T) = ker(T). Your vector space V must have dimension > 2. You may find it helpful to let V be a euclidean space and T a matrix transformation,
please help me with part a)
(1 point) Let V be the vector space P3 [x] of polynomials in x with degree less than 3 and W be the subspace W - span((-4)+ 5x2,4 +5x 7x2 a. Find a nonzero polynomial pr) in W b. Find a polynomial q(x) in V\ W. qx)1-2xA2+5
I really need help with solving this I have been struggling to understand it please help me thank you so much
3. (6 marks) Find an example of a vector space V, and a linear transformation T : V + V such that R(T) = ker(T). Your vector space V must have dimension > 2. You may find it helpful to let V be a euclidean space and T a matrix transformation, but that is not necessary. You must explain why your example works.
3. (6 marks) Find an example of a vector space V, and a linear transformation T : V +V such that R(T) = ker(T). Your vector space V must have dimension > 2. You may find it helpful to let V be a euclidean space and T a matrix transformation, but that is not necessary. You must explain why your example works.
Let V be the vector space of all sequences over R. Given (a1, a2, T,U V V by ) e V, define : ) ...) = (0, a1, 0, a2, 0, a3, . . . ) Тај, а2, аз, ад, 0, аз, (a1, a3, a5,.) and U(a1, a2, a3, a4, (a) Find N(T) and N(U) (b) Explain why T is onto, but not 1-1 (c) Explain why U is 1-1, but not onto.
(6) In each case V is a vector space, T: V- V is a linear transformation, and v is a vector in V. Determine whether the vector v is an eigenvector of T If so, give the associated eigenvalue Is v an eigenvector? If so, what is the eigenvalue? (b) T : M2(R) → M2(R) is given by [a+2b 2a +b c+d2d and V= Is v an eigenvector? If so, what is the eigenvalue? (c) T : R2 → R2,...
Let V P2(R) and let T V-V be a linear transformation defined by T(p)-q, where (x)(r p (r Let B = {x, 1 + x2, 2x-1} be a basis of V. Compute [TIB,B, and deduce if it is eigenvectors basis of