Linear Transformations: Properties & Examples


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question 1 of 3

There are _____ defining properties for a linear transformation.

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1. If u1 = 4, u2 = 5 and y = x2 + 3, what is T(u1 + u2) ?

2. If α = 6, u = 5 and T is 2x, what is T(αu) ?

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About This Quiz & Worksheet

Discover what you understand about linear transformations with these study assessments. Topics that the quiz will test include what a straight line is and what happens to a transformation that doesn't map a zero vector in the domain.

Quiz & Worksheet Goals

Use these tools to:

  • Identify the number of defining properties for a linear transformation
  • Interpret a given transformation
  • Select an accurate expression for a given vector

Skills Practiced

These tools will help you to practice the following skills:

  • Making connections - use understanding of the concept of a transformation and how it is connected to a vector in a domain
  • Defining key concepts - ensure that you can accurately define main phrases, such as a straight line and the defining properties for a linear transformation
  • Problem solving- use acquired knowledge to solve practice problems that ask you to identify if a given transformation

Additional Learning

Delve deeper into this area of study with the lesson entitled Linear Transformations: Properties & Examples. The lesson will cover the following study objectives:

  • Compare and contrast a domain and a range
  • Define transformation
  • Explain transformation properties
  • Interpret linear transformation on a graph
  • Understand how vectors are mapped