Suppose T: M2,2-P2 is a linear transformation whose action on a basis for M22 is as follows: 0 1 00 11 11 -1 -1 -2 -1 4x²+2x+1 7-8-9- T -2x²-2x-2 00 Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two matrices that have the same image under T. If T is not onto, show this by providing a polynomial in P2 that is not in the image of T. Use the character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1 T -x²+x+2 T T is one-to-one T is onto = -x²+x+2 T = =
Suppose T: M2,2-P2 is a linear transformation whose action on a basis for M22 is as follows: 0 1 00 11 11 -1 -1 -2 -1 4x²+2x+1 7-8-9- T -2x²-2x-2 00 Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two matrices that have the same image under T. If T is not onto, show this by providing a polynomial in P2 that is not in the image of T. Use the character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1 T -x²+x+2 T T is one-to-one T is onto = -x²+x+2 T = =
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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Transcribed Image Text:Suppose T: M22 P2 is a linear transformation whose action on a basis for M2 2 is as follows:
11
T
11
0 1
= -x2+x+2T
0 0
-1 -1
4x2 +2x+1 T
%3D
= -2x²-2x-2
0 -1
-2 -1
Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two matrices that have the same image under T. If
T is not onto, show this by providing a polynomial in P2 that is not in the image of T. Use the '^' character to indicate an exponent and x as the
variable for polynomials, e.g. 5x^2-2x+1
Tis one-to-one
Tis onto
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