Suppose T: M₂,2→R4 is a linear transformation whose action on a basis for M2,2 is as follows: T 33 33 -18 -1 - Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces each is a subset of, and then giving a set of appropriate vectors. Basis of Kernel is a Subset of M2,2 10 Number of Matrices: 1 Bker Basis of Image is a Subset of M2,2 Bim 00 Number of Matrices: 1 - 4 00 00

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose T: M2.2¬R4
is a linear transformation whose action on a basis for M2 2 is as follows:
-18
10
4
-2
0 0
33
T
3 3
-5
2
-1
-1
11
1
5
-1
Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces
each is a subset of, and then giving a set of appropriate vectors.
Basis of Kernel is a Subset of M2.2
Number of Matrices: 1
0 0
Bker
0 0
Basis of Image is a Subset of M2,2
Number of Matrices: 1
Bim
0 0
Transcribed Image Text:Suppose T: M2.2¬R4 is a linear transformation whose action on a basis for M2 2 is as follows: -18 10 4 -2 0 0 33 T 3 3 -5 2 -1 -1 11 1 5 -1 Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces each is a subset of, and then giving a set of appropriate vectors. Basis of Kernel is a Subset of M2.2 Number of Matrices: 1 0 0 Bker 0 0 Basis of Image is a Subset of M2,2 Number of Matrices: 1 Bim 0 0
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