Tutorial Sheet 6: Vector Spaces

 

 
Exercise 3

Let the vectors in ℝ3 be u1 = (1, 1, 1), u2 = (2, −2, −1), u3 = (1, 1, −1), and the set F = vect(u1, u2, u3).

  1. Is the family {u1, u2, u3} linearly independent?
  2. What is a basis of F?
Exercise 4

In ℝ3, consider the vectors u1 = (1, 1, 2) and u2 = (2, 4, 2).

  1. Show that these vectors are linearly dependent.
  2. Find a vector subspace of ℝ3 containing these vectors.
  3. Find a basis and deduce the dimension of this subspace.
آخر تعديل: السبت، 6 سبتمبر 2025، 8:05 PM