Let T be the linear transformation from M2,2 to the space of polynomials defined by:• Evaluate:bT= (a+b)x+cdTT51 311Based off these calculations, which ofand05are in the null space of-1 3T?• Name at least two specific polynomials which are in the image of T.

Answered: Let T be the linear transformation from…

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
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Let T be the linear transformation from M2,2 to the space of polynomials defined by: • Evaluate: b T = (a+b)x+c d T T 5 1 3 1 1 Based off these calculations, which of and 0 5 are in the null space of -1 3 T? • Name at least two specific polynomials which are in the image of T.