-8-B- 1. Let T be the linear transformation of Rª to Rª that takes and and takes and |2 a) Explain why there is one and only one linear transformation from R* to R* that does this. b) Find bases for both the kernel and the range of this linear transformation. c) Give an orthonormal basis for the kernel of this transformation. d) Indicate the matrix that would represent T with respect to the standard basis for R*.

-8-B- 1. Let T be the linear transformation of Rª to Rª that takes and and takes and |2 a) Explain why there is one and only one linear transformation from R* to R* that does this. b) Find bases for both the kernel and the range of this linear transformation. c) Give an orthonormal basis for the kernel of this transformation. d) Indicate the matrix that would represent T with respect to the standard basis for R*.

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

Let f : R? → R² be the linear transformation defined by -4 f(#) 4 -4 Let {(-1, –2), (3, 5)}, {(1,2), (1, 1)}, B C be two different bases for R?. Find the matrix [A% for f relative to the basis B in the domain and C in the codomain.
QUESTION 6 Let T be the linear transformation that takes: 2 and 5 and also 3 and 2 a) Explain why the vectors form a basis for R4 b) Find bases for both the kernel and the range of this linear transformation. c) Indicate the matrix that would represent T with respect to the standard basis of R4 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). 3222 2322 2232 2223 3 2, and
let The Linear Transformation given by T:P3toP2 T(ax³+bx²+cx+d)) = 3 ax²+2bx c find a basis for ker(T) and a basis for range(T). Also verify the dim ker(T) + dim {range(T)} = dim v
Let Let f: R² R2 be the linear transformation defined by [f]g = f(x) = {(-1,2), (2,-5)}, {(-1,2), (-1,3)}, be two different bases for R 2. Find the matrix [f] for f relative to the basis in the domain and in the codomain. = -5 5 -5 =
Let S be a linear transformation from R2 to R2 with associated matrix 11. Let T be a linear transformation from R2 to R2 with associated matrix -F A = C= B = 2 Determine the matrix C of the composition To S. -3 2] 0 2
Construct the matrix for the transformation T:R → R whose input is an R vector given in its standard coordinates and whose output is the last two components of xB only, given the basis B =
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)
Determine true or false: A linear transformation T is onto if and only if the columns of its standard matrix are linearly independent. True False
R3 → R3 be the linear transformation that projects u onto v = (6, −1, 1).Find a basis for the kernel of T.
defined by Let Let ƒ : R² → R² be the linear transformation [f] B = B C f(x) = = = 3 2 -2 - -3 x. be two different bases for R². Find the matrix [f] for f relative to the basis B in the domain and C in the codomain. {(-1,2), (3,-7)}, {{-1, -2), (3, 7)},