Description
Instructions: Read textbook pages 29 to 31 before working on the homework problems. Show all steps to get full credits.
1. Let
u =
1
2
, v =
1
1
, w =
−1
0
Prove that R
2 = span(u, v, w).
2. Prove that P
4 = span(−x
4
, x3
, −x
2
, x, −1).
3. Determine whether each of the following lists of vectors is linearly independent and provide justficiation.
(a)
1
1 + i
,
1 − i
2
in C
2
(b)
1
1
2
,
2
1
3
,
1
0
1
(c)
−1
2
0
,
2
−3
1
,
0
4
5
,
1
−2
−1
4. Provide a basis for the vector space of C
2×3 over C and show it is indeed a
basis.
5. Is
1
i
,
0
1
a basis of C
2
? Justify your answer.
