M340L EXAM 2B Your name:
SPRING, 2010
Dr. Schurle Your UTEID:
Show all your work on these pages. Be organized and neat. Your work should be your
own; there should be no talking, reading notes, checking laptops, using cellphones, .. . .
1. (10 points) Suppose that v1,v2,...,vpare vectors in a vector space Vand that H=
Span{v1,v2,...,vp}. Explain in detail how to get a basis for Hthat consists of vectors
from the list v1,v2,...,vp. The vector space Vmay not be any Rq, so you CANNOT
use columns or matrices or pivots in your explanation.
2. (10 points) Suppose His a n×nmatrix and the equation Hx=bis consistent for
every bin Rn. Does the equation Hx=0have a nontrivial solution? Justify your
answer.
