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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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+
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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