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uppose T: R3→M2 2 is a linear transformation whose action is defined by 5a+5b 3a+3b Tb = a+2b+4c 3a+3b Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a matrix in M22 that is not in the image of T.

uppose T: R3→M2 2 is a linear transformation whose action is defined by 5a+5b 3a+3b Tb = a+2b+4c 3a+3b Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a matrix in M22 that is not in the image of T.

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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uppose T: R→M22 is a linear transformation whose action is defined by a 5 a+5b 3a+3b Tb %3D a+2b+4c 3a+3b Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a matrix in M2 2 that is not in the image of T. T is one-to-one T is onto
Transcribed Image Text:uppose T: R→M22 is a linear transformation whose action is defined by a 5 a+5b 3a+3b Tb %3D a+2b+4c 3a+3b Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a matrix in M2 2 that is not in the image of T. T is one-to-one T is onto
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