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Suppose T: P2→R³ is a linear transformation whose action on a basis for P2 is as follows: 2 -8 T(x²+x+1) = -1 -6 T(2x) = 10 -4 2 4 Determine whether T is one-to-one and/or onto. If it is not one-to-one, 6 T(x²+x+2) = -6

Suppose T: P2→R³ is a linear transformation whose action on a basis for P2 is as follows: 2 -8 T(x²+x+1) = -1 -6 T(2x) = 10 -4 2 4 Determine whether T is one-to-one and/or onto. If it is not one-to-one, 6 T(x²+x+2) = -6

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: P2→R is a linear transformation whose action on a basis for P2 is as follows: 6 -8 T(x2+x+1) = -1 T(x²+x+2)=|-6 X 2 4 -4 | Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two polynomials that have the same image under T. If T is not onto, show this by providing a vector in R that is not in the image of T. Use the A' character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1 T is not one-to-one: T(0)= 0 and T(0)=|0 T is onto
Transcribed Image Text:Suppose T: P2→R is a linear transformation whose action on a basis for P2 is as follows: 6 -8 T(x2+x+1) = -1 T(x²+x+2)=|-6 X 2 4 -4 | Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two polynomials that have the same image under T. If T is not onto, show this by providing a vector in R that is not in the image of T. Use the A' character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1 T is not one-to-one: T(0)= 0 and T(0)=|0 T is onto
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