Suppose T:R-→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 R that is not in the range ofT.0 2 -6A =1 -3 60 -2 6

1. A transformation T:ℝn→ℝm is said to be linear if, Tx1+x2=Tx1+Tx2, ∀x1,x2∈ℝn Tcx=cTx, ∀x∈ℝn, c∈ℝ…

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, how 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 O 2 -6 A =1 -36 0 -2 6

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, how 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 O 2 -6 A =1 -36 0 -2 6

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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Question

Suppose T:R-→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 R that is not in the range of
T.
0 2 -6
A =1 -3 6
0 -2 6

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