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Suppose T: P3-R4 is a linear transformation whose action is defined by a+b+c+d -a-b-c-d 2a+2b+2c+2d -2a-2b-2c-2d T(ax3 +bx2+cx+d) = 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 P3 Bker = {0} Basis of Image is a Subset of P3 Bim= {0}

Suppose T: P3-R4 is a linear transformation whose action is defined by a+b+c+d -a-b-c-d 2a+2b+2c+2d -2a-2b-2c-2d T(ax3 +bx2+cx+d) = 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 P3 Bker = {0} Basis of Image is a Subset of P3 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: P3-R4 is a linear transformation whose action is defined by a+b+c+d -a-b-c-d 2a+2b+2c+2d -2a-2b-2c-2d T(ax3 +bx2+cx+d) = 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 P3 Bker = {0} Basis of Image is a Subset of P3 Bim {0} =
Transcribed Image Text:Suppose T: P3-R4 is a linear transformation whose action is defined by a+b+c+d -a-b-c-d 2a+2b+2c+2d -2a-2b-2c-2d T(ax3 +bx2+cx+d) = 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 P3 Bker = {0} Basis of Image is a Subset of P3 Bim {0} =
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