2) Let 4 =(0,5), 4, =(-3, -1) v; = (1,-5), v, =(-2,2) and let L be...
4, =(7,5), u =(-3,-1) 2) Let v = (1,-5), v = (-2,2) and let L be a linear operator on Rwhose matrix representation with respect to the ordered basis {u,,,) is A (3 -1 a) Determine the transition matrix (change of basis matrix) from {v, V, } to {u}. (Draw the commutative triangle). b) Find the matrix representation B, of L with respect to {v} by USING the similarity relation
11. =(7.5), #,(-3,-1) 2) Let = (1.-5). v. =(-2,2) and let L be a linear operator on R whose matrix representation with respect to the ordered basis . is a) Determine the transition matrix (change of basis matrix) from, v,to (1) (Draw the commutative triangle). 3 b) Find the matrix representation B, of L with respect to ,v} by USING the similarity relation
6. Let L be the linear operator mapping R3 into R3 defined by L(x) Ax, where A=12 0-2 and let 0 0 Find the transition matrix V corresponding to a change of basis from i,V2. vs) to e,e,es(standard basis for R3), and use it to determine the matrix B representing L with respect to (vi, V2. V
3. This example hopes to illustrate why the vector spaces the linear transformation are defined on are critical to the question of invertibility. Let L : → p, be defined by L(p)(t+1)p(t)-plt). (a) Given a basis of your choice, find a matrix representation of I with respect to your chosen basis (b) Show L: P+P is not invertible (e) Let V-span+21-4,+2t-8). It can be shown that L VV. Given an ordered basis for V of your choice, find a matrix...
i need the matlab code MATLAB: Change of Bases In this activity you will find a matrix representation with respect to two ordered bases for a linear transformation Find the matrix represenatation (Ty for the linear transformation T: R? – R? defined by *+ x [x-x2] with respect to the ordered bases = {2-01 C= = {@:3} First find 7(u) and T'(uz) the images of each of the basis vectors in B T(u) = T(u) =7 Create the augmented matrix...
Let L: R3 --> R3 be defined by Only need c-e solved. 6, (24 points) Let L : R3 → R3 be defined by (a) Find A, the standard matrix representation of f (b) Let 0 -2 2. Check that倔,G, u) is a basis of R3. (c) Find the transition matrix B from the ordered basis U (t, iz, a) to the standard basis {e, е,6). For questions (d) and (e), you can write your answer in terms of A...
1 6) Let L: R→ R* be defined as L(A) = A. (1 2) (1996.)A OC :) The standard basis for R2 is E = { Find the matrix representation of L with respect to E. (Hint: the matrix that represents the linear transformation, in this case, must be 4x4)
1 point) Read 'Diagonalization Changing to a Basis of Eigenvectors' before attempting this problem. Suppose that V is a 5-dimensional vector space. Let S -(vi,... , vs) be some ordered basis of V, and let T-(wi.... . ws) be some other ordered basis of V. Let L: V → V be a linear transformation. Let M be the matrix of L in the basis Sand et N be the matrix of L in the basis T. Decide whether each of...
1. Let L: P1(R) + P1(R) be a linear transformation given by L(a + bx) = a - b + (2a – b)x. Let S = {1, 2} and T = {1+x} be two basis for P1(R). (a) Find the matrix A of L with respect to basis S. (a) Find the matrix B of L with respect to basis T. (c) Find the matrix P obtained by expressing vectors in basis T in terms of vectors in basis (d)...
Let V be R, with thestandard inner product. If is a unitary operator on V, show that the matrix of U in the standard ordered basis is either cos θ -sin θ sin θ cos θ cos θ sin θ for some real θ, 0-θ < 2T. Let Us be the linear operator corresponding to the first matrix, i.e., Ue is rotation through the angle . Now convince yourself that every unitary operator on V is either a rotation, or...