Read about vector subspace | 2 Discussions | Page 1

  1. M

    Linear algebra problem related to vector subspace

    Homework Statement 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. Homework Equations The Attempt at a Solution 1. Put...
  2. M

    Vector subspace and linear transformation

    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...
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