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
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
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.
To show:
Given information:
a and b are real numbers.