Suppose T:R*R³ is the transformation induced by the following matrix A. 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 vector in R3 that is not in the range of T. 1 -4 3 -6 A =-2 8 -5 10 -2 8 -3 6 Tis one-to-one Tis onto
Suppose T:R*R³ is the transformation induced by the following matrix A. 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 vector in R3 that is not in the range of T. 1 -4 3 -6 A =-2 8 -5 10 -2 8 -3 6 Tis one-to-one Tis onto
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:R»R³ is the transformation induced by the following matrix A. 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 vector in R3 that is not in the range of T.
1 -4 3 -6
-2 8
A =
-5 10
-2 8 -3 6
T is one-to-one
T is onto
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