Let

Getting Started: To prove that T is the zero transformation, you need to show that

(i) Let v be an arbitrary vector in V such that

(ii) Use the definition and properties of linear transformations to rewrite

(iii) Use the fact that

Rivka Thorpe
2021-03-07
Answered

Let

Getting Started: To prove that T is the zero transformation, you need to show that

(i) Let v be an arbitrary vector in V such that

(ii) Use the definition and properties of linear transformations to rewrite

(iii) Use the fact that

You can still ask an expert for help

Anonym

Answered 2021-03-08
Author has **108** answers

Step 1

Let

Define the map,

To prove, the above defined map is a linear transformation.

Step 2

Therefore, the above defined map is a linear transformation and this is true for every vector in V.

Step 3

Let v be an arbitrary vector in V such that

Where,

The vector v can be written as such linear combination since

Apply the transformation T on both sides and use the fact that T is linear transformation.