Minh Nguyen                              			mtn8286
Week 5                                   			4.1.2

http://calclab.math.tamu.edu/~mtn8286/4_1_2.html

Problem:

Tell whether each of these sets is linearly dependent or linearly independent.

  (a)  {(1,0,1),(2,3,5),(1,1,2)}
  (b)  {(1,2),(1,-1),(0,3)}

Solution:

(a) Since the sets of vectors is a square matrix, there are two methods to 
    determine linear dependence or independence:

  Method 1:  Using determinant to find singularity.

	

  The set is nonsingular; there is some nontrivial linear combination of the
  set of vectors that vanishes.  Thus, the set is linearly dependent.

  Method 2:  Using row reduction.

	

  The set has a nontrivial solution:  Row 3 is a linear combination of Row 2.
  Thus, the set is linearly dependent.


(b) The set of vectors are non-square, we will use row reduction.

  	 

  The set has a nontrivial solution:  Row 3 is a linear combination of Row 2.
  Thus, the set is linearly dependent.