2.A linear transfarmation D:V→V is given withV = Sp £1,t, e, e, t.e ? vector space and D= d derivoteoperator.a-) Find the matrix corresponding to the lineartransformation D on the basis,2+6-) Define the D linear transformation. (D(x)=Y, X-f 4)and y f'(t)

Answered: Image /qna-images/answer/a1b10c82-d6b5-4668-9bd6-e43c617dd1b1.jpg

A linear trons.formation D:V→V is given with V = Sp £1, tiet, e, t.e*? vector space and D= d derivote operator. a-) Find the matrix transformation D on the basis of 0-$1itiet,e,t.e 6-) Define the D linear transformation. (D(x) =Y, X=f(4) and y f'(t) carresponding to the linear %3D

A linear trons.formation D:V→V is given with V = Sp £1, tiet, e, t.e*? vector space and D= d derivote operator. a-) Find the matrix transformation D on the basis of 0-$1itiet,e,t.e 6-) Define the D linear transformation. (D(x) =Y, X=f(4) and y f'(t) carresponding to the linear %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

10. Let T be the linear transformation from R3 to R$ that rotates every vector around the y-axis by radians, counterclockwise as viewed from the point (0,5, 0), and afterwards multiplies its length by 4. (a) Find the matrix of transformation T. (b) Calculate T((1, 2, 3)).
17.) show that I is linear transformation matrix that implemnts are not vectors but are entries in vectors ви! рин ва -ex'x 2 ton suldanum в the (ext_cxl ³x + xf = ¹²x) = (²x ¹ x ¹¹ x) I A =P (integer or decimal)
The cross product of two vectors in R' is defined by 日-屏 [b1 azb3 – azb2 ai a2 b2 azbı – aıb3 b3 aıb2 – azbı аз Let i . Find the matrix A of the linear transformation from R to R° given by T(7) = j x a. A = || ||
Suppose T : R^2 → R^2 is a linear transformation that does not alter e_i andwhich maps e_2 into e_2 + 2e_1, where e_i = (1,0), e_2 = (0,1). Find the transformation matrix T.Justify your answer.
4. Let B = {v1, v2, V3} and C = {w1, w2, w3} be bases for R3, with vectors defined below. -(:) -() --() v1 = V2 = V3 = and --(:) --E) --() 1 wi = , w2 = 1 , W3 = 1 Let L: R³ → R³ be the linear transformation defined by L: Find [L]B and [L]c, the matrices associated to L with respect to B and with respect to C.
Let B= (b,, b,, b,} and D= (d,, d,} be bases for vector spaces V and W, respectively. Let T :V- W be a linear transformation with the following properties. T(b,) = - 3d, +2d2, T(b2) = - 4d, + 4d2, T(b3) = 5d2 Find the matrix for T relative to B and D. The matrix for T relative to B and D isO.
8-3) show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2,... are not vectors but are entries in vectors a) T(x1, x2) = (2x2-3x1, x1-4x2, 0, x2) b) T(x1, x2, x3, x4) = 2x1 + 3x - 4x4 (T:R* → R)
4. Let V be a vector space. Prove that a) The zero transformation T(v) = b) The identity transformation T(v) = v for all v EV is a linear transformation. = 0 for all v EV is a linear transformation. CS Scanned with CamScanner
Suppose that T: R2 --> R2 is a linear transformation such that T (i) = (1,2) and T (j) =(2,4_ . Show that T is not onto by finding one vector in the codomain that is not the image of any vector in the domain. Is T one-to-one?
Suppose T: M2,2→→P2 is a linear transformation whose action on a basis for M2,2 is as follows: [18]-- Describe the action of T on a general matrix, using x as the variable for the polynomial and a, b, c, and d as constants. Use the character to indicate an exponent, e.g. ax^2-bx+c. = -2x+5 T = 0 1 1 -2 -2 = -x+4 T -4 -2 = 2x² +4x-26 T 00 = -2x²+2x+10