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Column vectors are written as rows, such as $\mathbf{x}=\left(x_{1}, x_{2}\right),$ and $T(\mathbf{x})$ is written as $T\left(x_{1}, x_{2}\right)$.Show that the transformation $T$ defined by $T\left(x_{1}, x_{2}\right)=$ $\left(2 x_{1}-3 x_{2}, x_{1}+4,5 x_{2}\right)$ is not linear.

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Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 8

Introduction to Linear Transformations

Introduction to Matrices

Campbell University

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

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03:26

Column vectors are written…

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In Exercises $17-20,$ show…

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02:39

01:48

02:41

Let $T_{1}: \mathbb{R}^{2}…

03:34

Let $V$ be a real inner pr…

02:36

Let $T : \mathbb{R}^{3} \r…

02:06

Let $\mathbf{v}_{1}$ and $…

01:23

Let $\left\{\mathbf{v}_{1}…

in this video, we're going to be working with the transformation t that we see defined here in row form. So this transformation T is interesting because of this right here, whenever you see a number that's not coefficient just a straight on constant with no variable x one or X two attached. Then there is something suspicious going on with the transformation. We would love the transformation t to be linear, but with this plus, four were no longer very sure. But what we do know about linear transformation tea is that if t mapping R M into our end is linear, then T would map the zero vector of our M into the zero vector of our end. Let's check that out for our transformation T well, right since t takes the zero vector from our to which would be 00 and replaces the zeros here, here, here, in here we obtain zero, four and zero, but this is not the zero vector because of the entry for here. So what's right that this is not the zero vector and this implies that t is not linear. So when we're looking for transformations tea and wondering if their linear or not always watch out for constants like this,

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