1. Let l: R2 → R³, l : x+ Ax, where k k %3D 2k –1 9 a.) Establish for which value of k, the linear function l is onto. b.) Establish for which value of k, the linear function l is one to one. c.) Establish for which value of k, it is dim Iml 1 and in this case, find a basis for Kerl.

1. Let l: R2 → R³, l : x+ Ax, where k k %3D 2k –1 9 a.) Establish for which value of k, the linear function l is onto. b.) Establish for which value of k, the linear function l is one to one. c.) Establish for which value of k, it is dim Iml 1 and in this case, find a basis for Kerl.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...

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Question

1. Let l: R2 R³, 1 : ¤ + Ax, where
k
A =
k
2k – 1 9
a.) Establish for which value of k, the linear function l is onto.
b.) Establish for which value of k, the linear function l is one to one.
c.) Establish for which value of k, it is dim Iml
1 and in this case, find a basis
for Kerl.

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