linear algebra

MAT 242 Written Homework #3

EP4.2, 4.3 / H4.2, 4.3 Due: October 20

Solve the following problems, showing any necessary work.

1. [1 point] Let W be the subspace spanned by

    −3 −1 1 −1

  ,

 

1 −1 2 −3

   . Which of the following vectors are in

W? (Note that the number of correct answers might be zero, one, two, three, or four.) 

5 17 12 1

  ,

 

26 −14 −20 18

  ,

  −13

1 −5 9

  ,

  −29 −7 5 −3

 

2. [1 point] Let ~v1 =

 

2 −5 −1 0

 , ~v2 =

  −2 1 1 5

 , ~v3 =

  −2 17 1

−15

 , and ~v4 =

 

2 2 3 −1

 . The set {~v1,~v2,~v3,~v4} is

linearly dependent. Find a nontrivial linear combination of these vectors that adds up to ~0.

3. [1 point] Let S =

   

0 2 1 −1

  ,

 

0 6 3 −3

  ,

 

0 4 2 −2

  ,

  −4 −2 2 2

  ,

  2 4 3 2

   . Find a basis for the subspace W spanned

by S, and the dimension of W .