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University of Toronto
Department of Mathematics
MAT223H1S
Linear Algebra I
Midterm Examination
February 28, 2008
W. AbouSalem, A. Hammerlindl, D. Krepski, S. Uppal
Duration: 1 hour 50 minutes
Last Name:
Given Name:
Student Number:
Tutorial Code:
No calculators or other aids are allowed.
FOR MARKER USE ONLY
Question
Mark
1
/8
2
/8
3
/8
4
/10
5
/10
6
/10
7
/6
TOTAL
/60
1 of 8
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View Full Document For each of the statements below, decide if it is true or false. Indicate your
answer by shading in the box corresponding to your choice. Justify your answer
by providing an appropriate proof or counter example.
[4]
1(a)
If the homogeneous system of linear equations
A
x
=
0
has only the trivial solution,
then
A
x
=
b
has a unique solution for every vector
b
.
true
false
[4]
1(b)
If
A
and
B
are square matrices and
both
AB
= 0 and
BA
= 0, then either
A
= 0 or
B
= 0.
true
false
2 of 8
For each of the statements below, decide if it is true or false. Indicate your
answer by shading in the box corresponding to your choice. Justify your answer
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This note was uploaded on 04/10/2010 for the course MAT MAT223 taught by Professor Uppal during the Fall '09 term at University of Toronto Toronto.
 Fall '09
 UPPAL
 Linear Algebra, Algebra

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