Suppose T:R3R3 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. [0 -1 -5 A= 0 1 1 1 4 Tis not one-to-one: TO and T0 T is not onto: is not the image of any x under T.

Suppose T:R3R3 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. [0 -1 -5 A= 0 1 1 1 4 Tis not one-to-one: TO and T0 T is not onto: 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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Pls help ASAP. Pls state that if T is one-to-one or T is not one-to-one and if it is not then pls give me the matrix fill in the blanks which you can see in the images. Also, pls tell me if T is onto or not onto and if it is not onto then pls fill in the matrix blanks. Pls do it right.

Suppose T:R3→R° 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 IR° that is not in the range of T.
-1
-5
A = |0 1
1 1
4
T is not one-to-one:
TO
0 and T|0
0.
0.
0.
T is not onto:
0 is not the image of any x under T.

Suppose T:R3→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 R that is not in the range of T.
0 -1 -5
A = 0 1
5
1 1
4
T is one-to-one
T is onto

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