I'll ask you if some "simple" sets of vectors in (fairly) low-dimensions are linearly dependent (or independent). Here are some examples.
Example 1: Suppose u1, u2, and u3 are these vectors in R4 shown in order as follows:
[4] [1 ] [0] [3] , [1 ] , [2] . [0] [-1] [0] [0] [0 ] [5]Is the set {u1, u2, u3} linearly independent?
Example 2: Suppose u1, u2, and u3 are these vectors in R5 shown in order as follows:
[1] [3] [-5] [2] [4] [-5] [3] , [5] , [-5] . [4] [6] [-5] [5] [7] [-5]Is the set {u1, u2, u3} linearly independent?
Example 3: Suppose u1, u2, u3, and u4 are these vectors in R4 shown in order as follows:
[431] [231] [2] [-1] [ 2 ] , [ 6 ] , [4] , [-2] . [260] [111] [2] [-1] [ 5 ] [ 8 ] [4] [-2]Is the set {u1, u2, u3, u4} linearly independent?
Example 4: Suppose u1, u2, u3, and u4 are these vectors in R5 shown in order as follows:
[3] [2] [0] [-3] [3] [2] [0] [-1] [2] , [6] , [0] , [-2] . [6] [1] [0] [-1] [5] [8] [0] [-2]Is the set {u1, u2, u3, u4} linearly independent?
Example 5: Suppose u1, u2, u3, u4, and u5 are these vectors in R2 shown in order as follows:
[1] , [4] , [5] , [3] , [2] . [1] [5] [8] [6] [3]Is the set {u1, u2, u3, u4, u5} linearly independent?
Maintained by greenfie@math.rutgers.edu and last modified 2/8/2011.