Suppose TR4 R³ is the transformation induced by the following matrix A. Determine whether I 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 I is not onto, show this by providing a vector in R³ that is not in the range of T. 3 -3 -9 -3 A 3 -2 -6 -4 = 30 0-6] T is not one-to-one: 0 0 0 To= 0 and To 0 0 I is not onto: 0 o is not the image of any x under T.
Suppose TR4 R³ is the transformation induced by the following matrix A. Determine whether I 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 I is not onto, show this by providing a vector in R³ that is not in the range of T. 3 -3 -9 -3 A 3 -2 -6 -4 = 30 0-6] T is not one-to-one: 0 0 0 To= 0 and To 0 0 I is not onto: 0 o is not the image of any x under 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:R4 R³ is the transformation induced by the following matrix A. Determine whether I 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 I is not onto, show this by providing a vector in R3 that is not in the range of T.
3 -3 -9 -3
A 3 -2 -6 -4
=
300-6
T is not one-to-one:
0
TO =
0
o and To 0
T is not onto:
o is not the image of any x under T.
0
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