MATH307-Group Homework 3 Solved

1.   Let

 

Prove that R2 = span(u,v,w).

2.   Prove that P4 = span(−x4,x3,−x2,x,−1).

3.   Determine whether each of the following lists of vectors is linearly independent and provide justficiation.

(a)

 

(b)

1 2 1

1,1,0

                                                                                         2           3           1

(c)

−1  2  0  1 

 2 ,−3,4,−2

                                                                            0               1             5            −1

4.   Provide a basis for the vector space of C2×3 over C and show it is indeed a basis.

5.   Is

 

a basis of C2? Justify your answer.