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Vector subspace and linear transformation

  1. Apr 23, 2015 #1
    X ={(x1,x2,x2 −x1,3x2):x1,x2 ∈R}
    f(x1,x2,x2 −x1,3x2)=(x1,x1,0,3x1)
    1. Find a basis for X.
    2. Find dim X.
    3. Find ker f and im f
    4. Find bases for ker f and im f
    5. Is f a bijection? Why?
    6. Find a diagonal matrix for f.

    My attempt:
    1. (1, 1, 0, 3) and (1, 2, 1, 6)
    2. Dim X = 2
    3. Ker f = 0, im f = X
    4. (0,0,0,0)
    5. I guess no, but do not know how to explain
    6. No idea
  2. jcsd
  3. Apr 24, 2015 #2


    Staff: Mentor

    Please start a new thread in the Homework & Coursework section (Calculus & Beyond subsection). Homework-type problems have to be posted there, using the homework template. See the Physics Forums rules here: https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/, listed under Homework Guidelines.

    When you start a new thread, please show more of your work, such as how you got the vectors of part 1, how you arrived at a dimension of 2 in part 2, and so on.
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