EL
1. Let A be an 18 X 16 matrix such that Am 0 has only the trivial solution.
follow lng questions:
*3 E 3?" $32," ,4": , E:
o What is the rank of A? E g"; E "
o If A21? 2 b is consistent for some 5 6 R18, will it have a unique solution?
A.0 Yes
2 WE? cfw_294.56% We Tee? 3 Ziieeeifi
1. Consider a homogeneous system of 2016 linear equations in 2000 unknowns. Which one of
the following is true?
A. The system can be inconsistent. )g Rafa: _
B. The system can never have innitely many solu
~ is? see cfw_5; E is 237235:
"ll
1. Consider a homogeneous system of 2010 linear equations in 1000 unknowns. Which one of
the following is true? ee ?
WCWRE
A. The system can be inconsistent. W? W;
B. The system can never have innitely many solutions.
C
2
Mm 34m M mi? full? leog
1. Let A be an 8 X 6 matrix such that A2: 2 0 has only the trivial solution. Answer the following
questions: cfw_4% a; E
g ,3; m W2: ;\ z
o What is the rank of A? Q "
a Is A21: 2 b consistent. for all b E R8?
A.0,Yes m X
66,3123
MAT 1341S: Introduction to Linear Algebra
Assignment 1
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Signature
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Please read these instructions carefully:
The table below is for the TA. Do not write in it.
The assignment has to be submitted
1. Which of the following are subspaces of R3?
U=cfw_(x2y? 513+313 Batmist, yER 33%? cfw_33:3
V:cfw_(2:gy22:e+y)$,yE:R $333 33333?
V=cfw_(xEy,z)l33+y20 S & cfw_553MQ @KVGJQX
: ~ 3: V: 3 = Z
3: cfw_<3 3133613 33233 333333337; 33:
A. U and V only
B. U and W