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-2 0 T 0 0 0 1 -10x3 +4x2 -4x+2 T 1 1 0 0 = 0 T 11 11 -5x3 +2x2-2x+1 T -5x3 +2x2-2x+1 = = 1 2 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 'A' 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 0 0 Bker 0 0 Basis of Image is a Subset of M22 Number of Matrices: 1 0 0 Bim 0 0

-2 0 T 0 0 0 1 -10x3 +4x2 -4x+2 T 1 1 0 0 = 0 T 11 11 -5x3 +2x2-2x+1 T -5x3 +2x2-2x+1 = = 1 2 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 'A' 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 0 0 Bker 0 0 Basis of Image is a Subset of M22 Number of Matrices: 1 0 0 Bim 0 0

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 3EQ
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Suppose T: M22→P3 is a linear transformation whose action on a basis for M2 2 is as follows: -2 0 T 0 0 0 1 = -10x3 +4x2 –4x+2 T 1 1 0 0 -5x3+2x² -2x+1 T 1 1 0 T 1 2 -5x3 +2x2 -2x+1 %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 M2.2 Number of Matrices: 1 Вкer 0 0 Basis of Image is a Subset of M2.2 Number of Matrices: 1 0 0 Bim 0 0
Transcribed Image Text:Suppose T: M22→P3 is a linear transformation whose action on a basis for M2 2 is as follows: -2 0 T 0 0 0 1 = -10x3 +4x2 –4x+2 T 1 1 0 0 -5x3+2x² -2x+1 T 1 1 0 T 1 2 -5x3 +2x2 -2x+1 %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 M2.2 Number of Matrices: 1 Вкer 0 0 Basis of Image is a Subset of M2.2 Number of Matrices: 1 0 0 Bim 0 0
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