Homework for §4.1
Determine whether the given set of vectors is linearly independent or linearly dependent. If it is
linearly dependent, write the last vector as a linear combination of the preceding vectors.
  
 

−1
1
 1

1.  6  ,  1  ,  20 


2
0
6

   

1
0
3


2.  3  ,  2  ,  −3 


−1
0
−1
.........................................................................................
Determine whether the following sets are subspaces of R3 . If V is a subspace, show that it is
closed under vector addition and scalar multiplication. If it is not, provide an example that
shows it is not closed under either vector addition or scalar multiplication.
3. V = {~x ∈ R3 : x1 + 2x2 = x3 }
4. V = {~x ∈ R3 : x1 x2 = x3 }