Suppose T: M2,2-P2 is a linear transformation whose action is defined by a b T c d = (-3b+3c+3d)x² +(5b-5c-5d)x+(a−31 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. If one your bases contains polynomials, give your answer as a comma-separated list of polynomials, using the character to indicate an exponent and x as the variable, e.g. 5x^2-2x+1 Basis of Kernel is a Subset of M2,2 Number of Matrices: 1 Bker = 00 00 Basis of Image is a Subset of P2 Bim = 0
Suppose T: M2,2-P2 is a linear transformation whose action is defined by a b T c d = (-3b+3c+3d)x² +(5b-5c-5d)x+(a−31 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. If one your bases contains polynomials, give your answer as a comma-separated list of polynomials, using the character to indicate an exponent and x as the variable, e.g. 5x^2-2x+1 Basis of Kernel is a Subset of M2,2 Number of Matrices: 1 Bker = 00 00 Basis of Image is a Subset of P2 Bim = 0
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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![Suppose T: M2,2→P2 is a linear transformation whose action is defined by
a b
(-3b+3c+3d)x² +(5b−5c−5d)x+(a−3b)
с
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. If one of
your bases contains polynomials, give your answer as a comma-separated list of polynomials, using the '^' character to indicate an exponent and x as the variable, e.g.
5x^2-2x+1
Basis of Kernel is a Subset of M2,2
Number of Matrices: 1
Bker
Bim
Basis of Image is a Subset of P2
0
00
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb1e9de9-a728-40ac-94a8-c6bce5f72bed%2F87ed0ba3-929b-44bd-a45f-ee6211a186d3%2Feys0avg_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose T: M2,2→P2 is a linear transformation whose action is defined by
a b
(-3b+3c+3d)x² +(5b−5c−5d)x+(a−3b)
с
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. If one of
your bases contains polynomials, give your answer as a comma-separated list of polynomials, using the '^' character to indicate an exponent and x as the variable, e.g.
5x^2-2x+1
Basis of Kernel is a Subset of M2,2
Number of Matrices: 1
Bker
Bim
Basis of Image is a Subset of P2
0
00
=
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