Suppose T:R³ R³ is the transformation given below. Determine whether Ti 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. 10x1-10x2 =x0x14x2 -2x1+2x2 xo Tx1 x2 T is not one-to-one: 0 0 0 ΤΟ = 0 and To 0 0 0 T is not onto: 0 = 0 0 0 0 is not the image of any x under T. 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Suppose T:R³ R³ is the transformation given below. 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.
xo
Tx1
x2
=
0
ΤΟ
0
T is not one-to-one:
10x1-10x2
|x05x14x2
-2x1+2x2
=
0
0
0 and TO
0
0
T is not onto:
0
= 0
0
0
0 is not the image of any x under T.
0
Transcribed Image Text:Suppose T:R³ R³ is the transformation given below. 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. xo Tx1 x2 = 0 ΤΟ 0 T is not one-to-one: 10x1-10x2 |x05x14x2 -2x1+2x2 = 0 0 0 and TO 0 0 T is not onto: 0 = 0 0 0 0 is not the image of any x under T. 0
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