3. Let T : R² → R² be defined by T = X Y -x+y x-y
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 69E: Find a basis for R2 that includes the vector (2,2).
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Question
![3. Let T: R2 R2 be defined by T =
i) Find a basis for Null(T)
ii) Find a basis for Range(T)<
-x y
-
([]) = [ + ]
[]=[:]
-x+y
a
- 16
-X+Y
0 0
a+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b4adcba-fb37-46fc-90a1-02680cb6583d%2F3aa307e5-5df6-46b5-bdf4-175cc983c215%2Ft0dh1yb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let T: R2 R2 be defined by T =
i) Find a basis for Null(T)
ii) Find a basis for Range(T)<
-x y
-
([]) = [ + ]
[]=[:]
-x+y
a
- 16
-X+Y
0 0
a+
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