Description
Instructions: Read textbook pages 29 to 31 before working on the homework problems. Show all steps to get full credits.
- Let
Prove that R2 = span(u,v,w).
- Prove that P4 = span(−x4,x3,−x2,x,−1).
- Determine whether each of the following lists of vectors is linearly independent and provide justficiation.
(a)
(b)
1 2 1
ï£1,ï£1,ï£0
2Â Â Â Â Â Â Â Â Â Â 3Â Â Â Â Â Â Â Â Â Â 1
(c)
−1  2  0  1 
ï£ 2 ,ï£âˆ’3,ï£4,ï£âˆ’2
0              1            5          −1
- Provide a basis for the vector space of C2×3 over C and show it is indeed a basis.
- Is
a basis of C2? Justify your answer.
1