University of Wisconsin-Madison Mathematics Department

Math 340 Elementary Matrix and Linear Algebra Lecturer: Arun Ram

Fall 2007

Homework 6: Due October 17, 2007

1. Do problems 1, 13, 17 and 19 on p187-188.
   
   
2. Do problems 7, 8, 9 and 13 on pages 196-197.
   
   
3. Do problems 5, 6, 9, 10 on page 206.
   
   
4. Do problems 3 and 4 on page 215.
   
   
5. Do problems 1, 2, 3, 5, 6, 7 on page 226.
   
   
6. Define the subspace generated by v₁,..., v_n.
   
   
7. Define span{v₁,..., v_n}.
   
   
8. Define linear combination.
   
   
9. Let V be a vector space and let v₁,..., v_n be elements of V. Show that the set of linear combinations of v₁,..., v_n is equal to span{v₁,..., v_n}.
   
   
10. Define linearly independent and basis and give some examples.