2. Does there exist a linear transformation T: R4 → R with nullspace {} € R¹ : 1 = 3x2, x3 = 4 ? ker (T) = x1 x2 x3 If yes, give an example of such a transformation. If not, give a proof that no such transfor- mation can exist.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 4CM
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2. Does there exist a linear transformation T: R4 → R with nullspace
X2
ker (T) =
-(13--
=
X3
X4
€ R¹ : £1 = 3x2, x3 = x4
If yes, give an example of such a transformation. If not, give a proof that no such transfor-
mation can exist.
Transcribed Image Text:2. Does there exist a linear transformation T: R4 → R with nullspace X2 ker (T) = -(13-- = X3 X4 € R¹ : £1 = 3x2, x3 = x4 If yes, give an example of such a transformation. If not, give a proof that no such transfor- mation can exist.
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