(E)- : a a 4 2 -6 Let L : R° → R² be defined by L 2 -1 3 1. Show that L is a linear transformation. 2. Find Ker L. 3. Find a basis for Ker L. What is the dimension of Ker L?
(E)- : a a 4 2 -6 Let L : R° → R² be defined by L 2 -1 3 1. Show that L is a linear transformation. 2. Find Ker L. 3. Find a basis for Ker L. What is the dimension of Ker L?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:()
a
a
4
2
-6
Let L : R' → R? be defined by L
-1
3
1. Show that L is a linear transformation.
2. Find Ker L.
3. Find a basis for Ker L. What is the dimension of Ker L?
4. Find Range L.
5. Find a basis for the Range L. What is the dimension of Range L?
6. Is L one-to-one? Why?
7. Is L onto? Why?
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