[Solved] MATH307 Group Homework3

Instructions: Read textbook pages 29 to 31 before working on the homework problems. Show all steps to get full credits.

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 C²³ over C and show it is indeed a basis.
5. Is

a basis of C²? Justify your answer.

1