Assignment #4: Algebra of Linear Transformations (back to full lecture notes)

In this assignment you will work with vector spaces and linear transformations.

  1. Complete the following argument.

    f,g R2R2, ∀ x,y R2,
         (f o g) is bijective   and
         xy
    implies
         # ...
    (g o f)(x)
    (g o f)(y)

  2. Complete the following argument.

    f R2R2,
    (
     
    12
    34
     
    ) represents (f)

    implies
         # ...
         (f) is bijective

  3. Complete the following argument.

    f,g R2R2,
    (
     
    12
    36
     
    ) represents (f)   and
    (
     
    24
    -1-2
     
    ) represents (g)

    implies
         # ...
    img(g)
    ker(f)

  4. Complete the following argument.

    f R2R2,
    (
     
    47
    25
     
    ) represents (f)

    implies
         # ...
         (f) is surjective