NAME(print): K r)
Math 203 Spring 2OLl-Exam 3
Instructor: J. Shapiro
Work carefully and neatly and remember that I cannot grade what I cannot read. You
must show ail relevant work in the appropriate space. You may receive no credit for a correct
answer if there is insufficient supporting work. Notes, books and graphing or programable
calculators are NOT ALLOWED.
[18pt] 1. Fill in the blanks with.4 (lways), S(ometimes), N(euer)so that the following are correct
statements.
(a) If dim V -- n and if S is a linearly independent subset of V with n vectors, then ,9
A spans I/.
(b)
(c)
(d)
If A is a 4 x 7 matrix, then the dimension of Nul A is Sequal to three.
The vector 3u * 2v is A in Span {r, r}.
If A is a non-invertible matrix, then the columns of ,4 are 5, N linearly inde-
pendent.
(e) If A is invertible, then Nul A A consists of only the zero vector.
(f) If dim V:6 and if .9 is asubset of V with 7 vectors, then ^9 t spans 7.
(f 'r \
[Spts] 2. Let H: 1l I | , ra > 01.
LLgI )
Show that 11 is not a subspace of R2
Lrt u= ( t\
\al
TLr^^ ba*h t^
fS*t u+U:
!A o+ L t'l
l-?
v: ( o
tl .
Oa^d V olt
(i) i/'| c te^r [1
