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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
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 =
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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