Name:
PID:
Discussion Section

No:
Time:
Midterm 1, Math 20F  Lecture B (Spring 2007)
Duration: 50 minutes
This is a closedbook exam. Calculators are not allowed. You can use one page of notes.
To get full credit you should support your answers.
There are four questions in this exam. All of the questions have two parts.
1.
Consider the system of linear equations
2
x
1
+ 4
x
2

x
3
= 2
x
1
+ 2
x
2
+
hx
3
=
b
where
h
and
b
are scalars.
a) (2.5 points)
Explain why the system cannot have a unique solution.
b) (2.5 points)
For what values of
h
and
b
the system is inconsistent.
#
Score
1
2
3
4
Total
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2.
The solution set of the homogeneous system
Ax
= 0 where
A
is a 3 by 3 matrix (corre
sponding to a system of three equations in three unknowns) is given by
span

1
1
0
,

1
0
1
.
Let
p
=
2
3

1
be a particular solution satisfying
Ax
=
b
for some given vector
b
of size 3.
a) (2 points)
Give a solution of the system
Ax
=
b
not equal to the particular solution
p
.
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