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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 3EQ

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