28.2. Examples of Linear Transformations

Try these first

1. 1.

   What is the identity transformation?

   Hint

   Think about what happens with a mirror.

2. 2.

   Describe the zero transformation.

   Hint

   Consider what happens when everything collapses to a point.

3. 3.

   What does the identity transformation do?

   • A. Maps to zero
   • B. Keeps vectors unchanged
   • C. Scales by a factor

   Hint

   Think about what happens to a vector when it's unchanged.

4. 4.

   True or False: A zero transformation will map all vectors to a point.

   • True
   • False

   Hint

   Consider what it means for everything to be one point.

5. 5.

   A vector x = [2, 3] undergoes a rotation transformation by θ = 45 degrees. What are the new coordinates?

   Hint

   Calculate the cosine and sine values for 45 degrees.

6. 6.

   If λ = -1 and x = [4, -2], apply a scaling transformation and state the new vector.

   Hint

   Multiply each component by the scalar λ.